{"id":9436,"date":"2017-05-02T22:30:52","date_gmt":"2017-05-02T22:30:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9436"},"modified":"2020-01-09T00:16:44","modified_gmt":"2020-01-09T00:16:44","slug":"identifying-multiples-of-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/identifying-multiples-of-numbers\/","title":{"raw":"Identifying Multiples of Numbers","rendered":"Identifying Multiples of Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Determine whether a given number is divisible by 2, 3, 5, or 10<\/li>\r\n<\/ul>\r\n<\/div>\r\nAnnie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn\u2019t have to count each one. She counts by twos: [latex]2,4,6,8,10,12[\/latex]. She has [latex]12[\/latex] shoes in her closet.\r\n\r\nThe numbers [latex]2,4,6,8,10,12[\/latex] are called multiples of [latex]2[\/latex]. Multiples of [latex]2[\/latex] can be written as the product of a counting number and [latex]2[\/latex]. The first six multiples of [latex]2[\/latex] are given below.\r\n<p style=\"text-align: left; padding-left: 30px;\">[latex]\\begin{array}{l}1\\cdot 2=2\\\\ 2\\cdot 2=4\\\\ 3\\cdot 2=6\\\\ 4\\cdot 2=8\\\\ 5\\cdot 2=10\\\\ 6\\cdot 2=12\\end{array}[\/latex]<\/p>\r\nA multiple of a number is the product of the number and a counting number. So a multiple of [latex]3[\/latex] would be the product of a counting number and [latex]3[\/latex]. Below are the first six multiples of [latex]3[\/latex].\r\n<p style=\"padding-left: 30px;\">[latex]\\begin{array}{l}1\\cdot 3=3\\\\ 2\\cdot 3=6\\\\ 3\\cdot 3=9\\\\ 4\\cdot 3=12\\\\ 5\\cdot 3=15\\\\ 6\\cdot 3=18\\end{array}[\/latex]<\/p>\r\nWe can find the multiples of any number by continuing this process. The table below\u00a0shows the multiples of [latex]2[\/latex] through [latex]9[\/latex] for the first twelve counting numbers.\r\n<table id=\"fs-id1946698\" summary=\"The table has nine rows and thirteen columns. The first row is a header row. The first row, first column labels the first row as the counting numbers. The remaining columns are labeled 1 through 12. Starting in the second row, the first column list the categories: \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th><strong>Counting Number<\/strong><\/th>\r\n<th>[latex]1[\/latex]<\/th>\r\n<th>[latex]2[\/latex]<\/th>\r\n<th>[latex]3[\/latex]<\/th>\r\n<th>[latex]4[\/latex]<\/th>\r\n<th>[latex]5[\/latex]<\/th>\r\n<th>[latex]6[\/latex]<\/th>\r\n<th>[latex]7[\/latex]<\/th>\r\n<th>[latex]8[\/latex]<\/th>\r\n<th>[latex]9[\/latex]<\/th>\r\n<th>[latex]10[\/latex]<\/th>\r\n<th>[latex]11[\/latex]<\/th>\r\n<th>[latex]12[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }2[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]14[\/latex]<\/td>\r\n<td>[latex]16[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]20[\/latex]<\/td>\r\n<td>[latex]22[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }3[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]21[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<td>[latex]27[\/latex]<\/td>\r\n<td>[latex]30[\/latex]<\/td>\r\n<td>[latex]33[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }4[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]16[\/latex]<\/td>\r\n<td>[latex]20[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<td>[latex]28[\/latex]<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>[latex]44[\/latex]<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }5[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<td>[latex]20[\/latex]<\/td>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>[latex]30[\/latex]<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>[latex]45[\/latex]<\/td>\r\n<td>[latex]50[\/latex]<\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<td>[latex]60[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }6[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<td>[latex]30[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>[latex]60[\/latex]<\/td>\r\n<td>[latex]66[\/latex]<\/td>\r\n<td>[latex]72[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }7[\/latex]<\/td>\r\n<td>[latex]7[\/latex]<\/td>\r\n<td>[latex]14[\/latex]<\/td>\r\n<td>[latex]21[\/latex]<\/td>\r\n<td>[latex]28[\/latex]<\/td>\r\n<td>[latex]35[\/latex]<\/td>\r\n<td>[latex]42[\/latex]<\/td>\r\n<td>[latex]49[\/latex]<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]70[\/latex]<\/td>\r\n<td>[latex]77[\/latex]<\/td>\r\n<td>[latex]84[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }8[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]16[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<td>[latex]32[\/latex]<\/td>\r\n<td>[latex]40[\/latex]<\/td>\r\n<td>[latex]48[\/latex]<\/td>\r\n<td>[latex]56[\/latex]<\/td>\r\n<td>[latex]64[\/latex]<\/td>\r\n<td>[latex]72[\/latex]<\/td>\r\n<td>[latex]80[\/latex]<\/td>\r\n<td>[latex]88[\/latex]<\/td>\r\n<td>[latex]96[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{Multiples of }9[\/latex]<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]27[\/latex]<\/td>\r\n<td>[latex]36[\/latex]<\/td>\r\n<td>[latex]45[\/latex]<\/td>\r\n<td>[latex]54[\/latex]<\/td>\r\n<td>[latex]63[\/latex]<\/td>\r\n<td>[latex]72[\/latex]<\/td>\r\n<td>[latex]81[\/latex]<\/td>\r\n<td>[latex]90[\/latex]<\/td>\r\n<td>[latex]99[\/latex]<\/td>\r\n<td>[latex]108[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox shaded\">\r\n<h3>Multiple of a Number<\/h3>\r\nA number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex].\r\n\r\n<\/div>\r\nRecognizing the patterns for multiples of [latex]2, 5, 10, \\text{and }3[\/latex] will be helpful to you as you continue in this course.\r\n\r\nDoing the Manipulative Mathematics activity \"Multiples\" will help you develop a better understanding of multiples.\r\nThe table below\u00a0shows the counting numbers from [latex]1[\/latex] to [latex]50[\/latex]. Multiples of [latex]2[\/latex] are highlighted. Do you notice a pattern?\r\n\r\nMultiples of [latex]2[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220005\/CNX_BMath_Figure_02_04_001.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 2 are highlighted in blue.\" \/>\r\n\r\nThe last digit of each highlighted number in the table\u00a0is either [latex]0, 2, 4, 6, \\text{or }8[\/latex]. This is true for the product of [latex]2[\/latex] and any counting number. So, to tell if any number is a multiple of [latex]2[\/latex] look at the last digit. If it is [latex]0, 2, 4, 6, \\text{or }8[\/latex], then the number is a multiple of [latex]2[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each of the following is a multiple of [latex]2\\text{:}[\/latex]\r\n<ol>\r\n \t<li>[latex]489[\/latex]<\/li>\r\n \t<li>[latex]3,714[\/latex]<\/li>\r\n<\/ol>\r\nSolution:\r\n<table id=\"eip-id1168468413253\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]489[\/latex] a multiple of [latex]2[\/latex]?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]0, 2, 4, 6, \\text{ or } 8[\/latex] ?<\/td>\r\n<td>No.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]489[\/latex] is not a multiple of [latex]2[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469557564\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]3,714[\/latex]a multiple of [latex]2[\/latex]?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]0, 2, 4, 6, \\text{ or } 8[\/latex] ?<\/td>\r\n<td>Yes.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3,714[\/latex] is a multiple of [latex]2[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145363&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nNow let\u2019s look at multiples of [latex]5[\/latex]. The table below highlights all of the multiples of [latex]5[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]. What do you notice about the multiples of [latex]5?[\/latex]\r\n\r\nMultiples of [latex]5[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220007\/CNX_BMath_Figure_02_04_002.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 5 are highlighted in blue.\" \/>\r\n\r\nAll multiples of [latex]5[\/latex] end with either [latex]5[\/latex] or [latex]0[\/latex]. Just like we identify multiples of [latex]2[\/latex] by looking at the last digit, we can identify multiples of [latex]5[\/latex] by looking at the last digit.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each of the following is a multiple of [latex]5\\text{:}[\/latex]\r\n<ol>\r\n \t<li>[latex]579[\/latex]<\/li>\r\n \t<li>[latex]880[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"984942\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"984942\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466183262\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]579[\/latex] a multiple of [latex]5[\/latex] ?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]5\\text{ or }0[\/latex] ?<\/td>\r\n<td>No.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]579[\/latex] is not a multiple of [latex]5[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469479124\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]880[\/latex] a multiple of [latex]5[\/latex] ?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]5\\text{ or }0[\/latex] ?<\/td>\r\n<td>Yes.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]880[\/latex] is a multiple of [latex]5[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145413&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nThe table below\u00a0highlights the multiples of [latex]10[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]. All multiples of [latex]10[\/latex] all end with a zero.\r\n\r\nMultiples of [latex]10[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220009\/CNX_BMath_Figure_02_04_003.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 10 are highlighted in blue.\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each of the following is a multiple of [latex]10\\text{:}[\/latex]\r\n<ol>\r\n \t<li>[latex]425[\/latex]<\/li>\r\n \t<li>[latex]350[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"432922\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"432922\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466058608\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]425[\/latex] a multiple of [latex]10[\/latex] ?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]0[\/latex] ?<\/td>\r\n<td>No.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]425[\/latex] is not a multiple of [latex]10[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468276774\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]350[\/latex] a multiple of [latex]10[\/latex] ?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is the last digit [latex]0[\/latex] ?<\/td>\r\n<td>Yes.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]350[\/latex] is a multiple of [latex]10[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145417&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nThe table below\u00a0highlights multiples of [latex]3[\/latex]. The pattern for multiples of [latex]3[\/latex] is not as obvious as the patterns for multiples of [latex]2,5,\\text{and }10[\/latex].\r\n\r\nMultiples of [latex]3[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220010\/CNX_BMath_Figure_02_04_004.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 3 are highlighted in blue.\" \/>\r\n\r\nUnlike the other patterns we\u2019ve examined so far, this pattern does not involve the last digit. The pattern for multiples of [latex]3[\/latex] is based on the sum of the digits. If the sum of the digits of a number is a multiple of [latex]3[\/latex], then the number itself is a multiple of [latex]3[\/latex]. See the example below.\r\n<table id=\"fs-id2670625\" style=\"width: 85%;\" summary=\"This table has two rows and nine columns. The first column labels the two rows. The first row is \">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\\mathbf{\\text{Multiple of 3}}[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]21[\/latex]<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\mathbf{\\text{Sum of digits}}[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]9[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1+2\\hfill \\\\ \\hfill 3\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1+5\\hfill \\\\ \\hfill 6\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 1+8\\hfill \\\\ \\hfill 9\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 2+1\\hfill \\\\ \\hfill 3\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{c}\\hfill 2+4\\hfill \\\\ \\hfill 6\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nConsider the number [latex]42[\/latex]. The digits are [latex]4[\/latex] and [latex]2[\/latex], and their sum is [latex]4+2=6[\/latex]. Since [latex]6[\/latex] is a multiple of [latex]3[\/latex], we know that [latex]42[\/latex] is also a multiple of [latex]3[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each of the given numbers is a multiple of [latex]3\\text{:}[\/latex]\r\n<ol>\r\n \t<li>[latex]645[\/latex]<\/li>\r\n \t<li>[latex]10,519[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"683066\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"683066\"]\r\n\r\nSolution:\r\n1. Is [latex]645[\/latex] a multiple of [latex]3?[\/latex]\r\n<table id=\"eip-id1168467261275\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Find the sum of the digits.<\/td>\r\n<td>[latex]6+4+5=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]15[\/latex] a multiple of [latex]3[\/latex] ?<\/td>\r\n<td>Yes.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If we're not sure, we could add its digits to find out. We can check it by dividing [latex]645\\text{ by }3[\/latex].<\/td>\r\n<td>[latex]645\\div 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The quotient is [latex]215[\/latex].<\/td>\r\n<td>[latex]3\\cdot 215=645[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. Is [latex]10,519[\/latex] a multiple of [latex]3?[\/latex]\r\n<table id=\"eip-id1168466267838\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Find the sum of the digits.<\/td>\r\n<td>[latex]1+0+5+1+9=16[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is [latex]16[\/latex] a multiple of [latex]3[\/latex] ?<\/td>\r\n<td>No.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So [latex]10,519[\/latex] is not a multiple of [latex]3[\/latex] either..<\/td>\r\n<td>[latex]645\\div 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We can check this by dividing by [latex]10,519\\text{ by }3[\/latex].<\/td>\r\n<td>[latex]\\begin{array}{c}3,506\\text{R}1\\\\ \\hfill 3\\overline{)10,519}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen we divide [latex]10,519[\/latex] by [latex]3[\/latex], we do not get a counting number, so [latex]10,519[\/latex] is not the product of a counting number and [latex]3[\/latex]. It is not a multiple of [latex]3[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145418&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\nLook back at the charts where you highlighted the multiples of [latex]2[\/latex], of [latex]5[\/latex], and of [latex]10[\/latex]. Notice that the multiples of [latex]10[\/latex] are the numbers that are multiples of both [latex]2[\/latex] and [latex]5[\/latex]. That is because [latex]10=2\\cdot 5[\/latex]. Likewise, since [latex]6=2\\cdot 3[\/latex], the multiples of [latex]6[\/latex] are the numbers that are multiples of both [latex]2[\/latex] and [latex]3[\/latex].\r\n\r\nThe following video shows how to determine the first four multiples of 6.\r\n\r\nhttps:\/\/youtu.be\/mkEWqspRVKk\r\n<h3>Use Common Divisibility Tests<\/h3>\r\nAnother way to say that [latex]375[\/latex] is a multiple of [latex]5[\/latex] is to say that [latex]375[\/latex] is divisible by [latex]5[\/latex]. In fact, [latex]375\\div 5[\/latex] is [latex]75[\/latex], so [latex]375[\/latex] is [latex]5\\cdot 75[\/latex]. Notice in the last example\u00a0that [latex]10,519[\/latex] is not a multiple [latex]3[\/latex]. When we divided [latex]10,519[\/latex] by [latex]3[\/latex] we did not get a counting number, so [latex]10,519[\/latex] is not divisible by [latex]3[\/latex].\r\n<div class=\"textbox shaded\">\r\n<h3>Divisibility<\/h3>\r\nIf a number [latex]m[\/latex] is a multiple of [latex]n[\/latex], then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex].\r\n\r\n<\/div>\r\nSince multiplication and division are inverse operations, the patterns of multiples that we found can be used as divisibility tests. The table below\u00a0summarizes divisibility tests for some of the counting numbers between one and ten.\r\n<table id=\"fs-id2134771\" style=\"width: 85%;\" summary=\"This table has five rows and two columns. The first row is a header row that labels each column. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"2\"><strong>Divisibility Tests<\/strong><\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th><strong>A number is divisible by<\/strong><\/th>\r\n<th><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>if the last digit is [latex]0,2,4,6,\\text{or }8[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>if the sum of the digits is divisible by [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>if the last digit is [latex]5[\/latex] or [latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>if divisible by both [latex]2[\/latex] and [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>if the last digit is [latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether [latex]1,290[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].\r\n[reveal-answer q=\"289804\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"289804\"]\r\n\r\nSolution:\r\nThe table below\u00a0applies the divisibility tests to [latex]1,290[\/latex]. In the far right column, we check the results of the divisibility tests by seeing if the quotient is a whole number.\r\n<table id=\"fs-id1405269\" style=\"width: 85%;\" summary=\"This table has five rows and four columns. The first row is a header row that labels each column. The columns are labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th><strong>Divisible by\u2026?<\/strong><\/th>\r\n<th><strong>Test<\/strong><\/th>\r\n<th><strong>Divisible?<\/strong><\/th>\r\n<th><strong>Check<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>Is last digit [latex]0,2,4,6,\\text{or }8?[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]1290\\div 2=645[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\text{Is sum of digits divisible by }3?[\/latex]\r\n\r\n[latex]1+2+9+0=12[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]1290\\div 3=430[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>Is last digit [latex]5[\/latex] or [latex]0?[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]1290\\div 5=258[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>Is last digit [latex]0?[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]1290\\div 10=129[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThus, [latex]1,290[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145433&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether [latex]5,625[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].\r\n[reveal-answer q=\"246871\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"246871\"]\r\n\r\nSolution:\r\nThe table below\u00a0applies the divisibility tests to [latex]5,625[\/latex] and tests the results by finding the quotients.\r\n<table id=\"fs-id1970659\" style=\"width: 85%;\" summary=\"This table has five rows and four columns. The first row is a header row that labels each column. The columns are labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th><strong>Divisible by\u2026?<\/strong><\/th>\r\n<th><strong>Test<\/strong><\/th>\r\n<th><strong>Divisible?<\/strong><\/th>\r\n<th><strong>Check<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>Is last digit [latex]0,2,4,6,\\text{or }8?[\/latex] <em>No.<\/em><\/td>\r\n<td>no<\/td>\r\n<td>[latex]5625\\div 2=2812.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]\\text{Is sum of digits divisible by }3?[\/latex]\r\n\r\n[latex]5+6+2+5=18[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]5625\\div 3=1875[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>Is last digit is [latex]5[\/latex] or [latex]0?[\/latex] <em>Yes.<\/em><\/td>\r\n<td>yes<\/td>\r\n<td>[latex]5625\\div 5=1125[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>Is last digit [latex]0?[\/latex] <em>No.<\/em><\/td>\r\n<td>no<\/td>\r\n<td>[latex]5625\\div 10=562.5[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThus, [latex]5,625[\/latex] is divisible by [latex]3[\/latex] and [latex]5[\/latex], but not [latex]2[\/latex], or [latex]10[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]145433[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video lesson shows how to determine whether a number is divisible by [latex]2,3,4,5,6,8,9,10[\/latex]\r\n\r\nhttps:\/\/youtu.be\/i16N01IdIhk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine whether a given number is divisible by 2, 3, 5, or 10<\/li>\n<\/ul>\n<\/div>\n<p>Annie is counting the shoes in her closet. The shoes are matched in pairs, so she doesn\u2019t have to count each one. She counts by twos: [latex]2,4,6,8,10,12[\/latex]. She has [latex]12[\/latex] shoes in her closet.<\/p>\n<p>The numbers [latex]2,4,6,8,10,12[\/latex] are called multiples of [latex]2[\/latex]. Multiples of [latex]2[\/latex] can be written as the product of a counting number and [latex]2[\/latex]. The first six multiples of [latex]2[\/latex] are given below.<\/p>\n<p style=\"text-align: left; padding-left: 30px;\">[latex]\\begin{array}{l}1\\cdot 2=2\\\\ 2\\cdot 2=4\\\\ 3\\cdot 2=6\\\\ 4\\cdot 2=8\\\\ 5\\cdot 2=10\\\\ 6\\cdot 2=12\\end{array}[\/latex]<\/p>\n<p>A multiple of a number is the product of the number and a counting number. So a multiple of [latex]3[\/latex] would be the product of a counting number and [latex]3[\/latex]. Below are the first six multiples of [latex]3[\/latex].<\/p>\n<p style=\"padding-left: 30px;\">[latex]\\begin{array}{l}1\\cdot 3=3\\\\ 2\\cdot 3=6\\\\ 3\\cdot 3=9\\\\ 4\\cdot 3=12\\\\ 5\\cdot 3=15\\\\ 6\\cdot 3=18\\end{array}[\/latex]<\/p>\n<p>We can find the multiples of any number by continuing this process. The table below\u00a0shows the multiples of [latex]2[\/latex] through [latex]9[\/latex] for the first twelve counting numbers.<\/p>\n<table id=\"fs-id1946698\" summary=\"The table has nine rows and thirteen columns. The first row is a header row. The first row, first column labels the first row as the counting numbers. The remaining columns are labeled 1 through 12. Starting in the second row, the first column list the categories:\">\n<thead>\n<tr valign=\"top\">\n<th><strong>Counting Number<\/strong><\/th>\n<th>[latex]1[\/latex]<\/th>\n<th>[latex]2[\/latex]<\/th>\n<th>[latex]3[\/latex]<\/th>\n<th>[latex]4[\/latex]<\/th>\n<th>[latex]5[\/latex]<\/th>\n<th>[latex]6[\/latex]<\/th>\n<th>[latex]7[\/latex]<\/th>\n<th>[latex]8[\/latex]<\/th>\n<th>[latex]9[\/latex]<\/th>\n<th>[latex]10[\/latex]<\/th>\n<th>[latex]11[\/latex]<\/th>\n<th>[latex]12[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }2[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]14[\/latex]<\/td>\n<td>[latex]16[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]20[\/latex]<\/td>\n<td>[latex]22[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }3[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]15[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]21[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<td>[latex]27[\/latex]<\/td>\n<td>[latex]30[\/latex]<\/td>\n<td>[latex]33[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }4[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]16[\/latex]<\/td>\n<td>[latex]20[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<td>[latex]28[\/latex]<\/td>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]40[\/latex]<\/td>\n<td>[latex]44[\/latex]<\/td>\n<td>[latex]48[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }5[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]15[\/latex]<\/td>\n<td>[latex]20[\/latex]<\/td>\n<td>[latex]25[\/latex]<\/td>\n<td>[latex]30[\/latex]<\/td>\n<td>[latex]35[\/latex]<\/td>\n<td>[latex]40[\/latex]<\/td>\n<td>[latex]45[\/latex]<\/td>\n<td>[latex]50[\/latex]<\/td>\n<td>[latex]55[\/latex]<\/td>\n<td>[latex]60[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }6[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<td>[latex]30[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]42[\/latex]<\/td>\n<td>[latex]48[\/latex]<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>[latex]60[\/latex]<\/td>\n<td>[latex]66[\/latex]<\/td>\n<td>[latex]72[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }7[\/latex]<\/td>\n<td>[latex]7[\/latex]<\/td>\n<td>[latex]14[\/latex]<\/td>\n<td>[latex]21[\/latex]<\/td>\n<td>[latex]28[\/latex]<\/td>\n<td>[latex]35[\/latex]<\/td>\n<td>[latex]42[\/latex]<\/td>\n<td>[latex]49[\/latex]<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]70[\/latex]<\/td>\n<td>[latex]77[\/latex]<\/td>\n<td>[latex]84[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }8[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]16[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<td>[latex]32[\/latex]<\/td>\n<td>[latex]40[\/latex]<\/td>\n<td>[latex]48[\/latex]<\/td>\n<td>[latex]56[\/latex]<\/td>\n<td>[latex]64[\/latex]<\/td>\n<td>[latex]72[\/latex]<\/td>\n<td>[latex]80[\/latex]<\/td>\n<td>[latex]88[\/latex]<\/td>\n<td>[latex]96[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{Multiples of }9[\/latex]<\/td>\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]27[\/latex]<\/td>\n<td>[latex]36[\/latex]<\/td>\n<td>[latex]45[\/latex]<\/td>\n<td>[latex]54[\/latex]<\/td>\n<td>[latex]63[\/latex]<\/td>\n<td>[latex]72[\/latex]<\/td>\n<td>[latex]81[\/latex]<\/td>\n<td>[latex]90[\/latex]<\/td>\n<td>[latex]99[\/latex]<\/td>\n<td>[latex]108[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox shaded\">\n<h3>Multiple of a Number<\/h3>\n<p>A number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex].<\/p>\n<\/div>\n<p>Recognizing the patterns for multiples of [latex]2, 5, 10, \\text{and }3[\/latex] will be helpful to you as you continue in this course.<\/p>\n<p>Doing the Manipulative Mathematics activity &#8220;Multiples&#8221; will help you develop a better understanding of multiples.<br \/>\nThe table below\u00a0shows the counting numbers from [latex]1[\/latex] to [latex]50[\/latex]. Multiples of [latex]2[\/latex] are highlighted. Do you notice a pattern?<\/p>\n<p>Multiples of [latex]2[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220005\/CNX_BMath_Figure_02_04_001.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 2 are highlighted in blue.\" \/><\/p>\n<p>The last digit of each highlighted number in the table\u00a0is either [latex]0, 2, 4, 6, \\text{or }8[\/latex]. This is true for the product of [latex]2[\/latex] and any counting number. So, to tell if any number is a multiple of [latex]2[\/latex] look at the last digit. If it is [latex]0, 2, 4, 6, \\text{or }8[\/latex], then the number is a multiple of [latex]2[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each of the following is a multiple of [latex]2\\text{:}[\/latex]<\/p>\n<ol>\n<li>[latex]489[\/latex]<\/li>\n<li>[latex]3,714[\/latex]<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468413253\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]489[\/latex] a multiple of [latex]2[\/latex]?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]0, 2, 4, 6, \\text{ or } 8[\/latex] ?<\/td>\n<td>No.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]489[\/latex] is not a multiple of [latex]2[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469557564\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]3,714[\/latex]a multiple of [latex]2[\/latex]?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]0, 2, 4, 6, \\text{ or } 8[\/latex] ?<\/td>\n<td>Yes.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]3,714[\/latex] is a multiple of [latex]2[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145363&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>Now let\u2019s look at multiples of [latex]5[\/latex]. The table below highlights all of the multiples of [latex]5[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]. What do you notice about the multiples of [latex]5?[\/latex]<\/p>\n<p>Multiples of [latex]5[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220007\/CNX_BMath_Figure_02_04_002.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 5 are highlighted in blue.\" \/><\/p>\n<p>All multiples of [latex]5[\/latex] end with either [latex]5[\/latex] or [latex]0[\/latex]. Just like we identify multiples of [latex]2[\/latex] by looking at the last digit, we can identify multiples of [latex]5[\/latex] by looking at the last digit.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each of the following is a multiple of [latex]5\\text{:}[\/latex]<\/p>\n<ol>\n<li>[latex]579[\/latex]<\/li>\n<li>[latex]880[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q984942\">Show Solution<\/span><\/p>\n<div id=\"q984942\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466183262\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]579[\/latex] a multiple of [latex]5[\/latex] ?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]5\\text{ or }0[\/latex] ?<\/td>\n<td>No.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]579[\/latex] is not a multiple of [latex]5[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469479124\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]880[\/latex] a multiple of [latex]5[\/latex] ?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]5\\text{ or }0[\/latex] ?<\/td>\n<td>Yes.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]880[\/latex] is a multiple of [latex]5[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145413&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>The table below\u00a0highlights the multiples of [latex]10[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]. All multiples of [latex]10[\/latex] all end with a zero.<\/p>\n<p>Multiples of [latex]10[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220009\/CNX_BMath_Figure_02_04_003.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 10 are highlighted in blue.\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each of the following is a multiple of [latex]10\\text{:}[\/latex]<\/p>\n<ol>\n<li>[latex]425[\/latex]<\/li>\n<li>[latex]350[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q432922\">Show Solution<\/span><\/p>\n<div id=\"q432922\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466058608\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]425[\/latex] a multiple of [latex]10[\/latex] ?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]0[\/latex] ?<\/td>\n<td>No.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]425[\/latex] is not a multiple of [latex]10[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468276774\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is [latex]350[\/latex] a multiple of [latex]10[\/latex] ?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is the last digit [latex]0[\/latex] ?<\/td>\n<td>Yes.<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]350[\/latex] is a multiple of [latex]10[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145417&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>The table below\u00a0highlights multiples of [latex]3[\/latex]. The pattern for multiples of [latex]3[\/latex] is not as obvious as the patterns for multiples of [latex]2,5,\\text{and }10[\/latex].<\/p>\n<p>Multiples of [latex]3[\/latex] between [latex]1[\/latex] and [latex]50[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220010\/CNX_BMath_Figure_02_04_004.png\" alt=\"The image shows a chart with five rows and ten columns. The first row lists the numbers from 1 to 10. The second row lists the numbers from 11 to 20. The third row lists the numbers from 21 to 30. The fourth row lists the numbers from 31 and 40. The fifth row lists the numbers from 41 to 50. All factors of 3 are highlighted in blue.\" \/><\/p>\n<p>Unlike the other patterns we\u2019ve examined so far, this pattern does not involve the last digit. The pattern for multiples of [latex]3[\/latex] is based on the sum of the digits. If the sum of the digits of a number is a multiple of [latex]3[\/latex], then the number itself is a multiple of [latex]3[\/latex]. See the example below.<\/p>\n<table id=\"fs-id2670625\" style=\"width: 85%;\" summary=\"This table has two rows and nine columns. The first column labels the two rows. The first row is\">\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\\mathbf{\\text{Multiple of 3}}[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]15[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]21[\/latex]<\/td>\n<td>[latex]24[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\mathbf{\\text{Sum of digits}}[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]9[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1+2\\hfill \\\\ \\hfill 3\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1+5\\hfill \\\\ \\hfill 6\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 1+8\\hfill \\\\ \\hfill 9\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 2+1\\hfill \\\\ \\hfill 3\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}\\hfill 2+4\\hfill \\\\ \\hfill 6\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Consider the number [latex]42[\/latex]. The digits are [latex]4[\/latex] and [latex]2[\/latex], and their sum is [latex]4+2=6[\/latex]. Since [latex]6[\/latex] is a multiple of [latex]3[\/latex], we know that [latex]42[\/latex] is also a multiple of [latex]3[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each of the given numbers is a multiple of [latex]3\\text{:}[\/latex]<\/p>\n<ol>\n<li>[latex]645[\/latex]<\/li>\n<li>[latex]10,519[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q683066\">Show Solution<\/span><\/p>\n<div id=\"q683066\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\n1. Is [latex]645[\/latex] a multiple of [latex]3?[\/latex]<\/p>\n<table id=\"eip-id1168467261275\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find the sum of the digits.<\/td>\n<td>[latex]6+4+5=15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Is [latex]15[\/latex] a multiple of [latex]3[\/latex] ?<\/td>\n<td>Yes.<\/td>\n<\/tr>\n<tr>\n<td>If we&#8217;re not sure, we could add its digits to find out. We can check it by dividing [latex]645\\text{ by }3[\/latex].<\/td>\n<td>[latex]645\\div 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The quotient is [latex]215[\/latex].<\/td>\n<td>[latex]3\\cdot 215=645[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. Is [latex]10,519[\/latex] a multiple of [latex]3?[\/latex]<\/p>\n<table id=\"eip-id1168466267838\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>Find the sum of the digits.<\/td>\n<td>[latex]1+0+5+1+9=16[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Is [latex]16[\/latex] a multiple of [latex]3[\/latex] ?<\/td>\n<td>No.<\/td>\n<\/tr>\n<tr>\n<td>So [latex]10,519[\/latex] is not a multiple of [latex]3[\/latex] either..<\/td>\n<td>[latex]645\\div 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>We can check this by dividing by [latex]10,519\\text{ by }3[\/latex].<\/td>\n<td>[latex]\\begin{array}{c}3,506\\text{R}1\\\\ \\hfill 3\\overline{)10,519}\\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When we divide [latex]10,519[\/latex] by [latex]3[\/latex], we do not get a counting number, so [latex]10,519[\/latex] is not the product of a counting number and [latex]3[\/latex]. It is not a multiple of [latex]3[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145418&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>Look back at the charts where you highlighted the multiples of [latex]2[\/latex], of [latex]5[\/latex], and of [latex]10[\/latex]. Notice that the multiples of [latex]10[\/latex] are the numbers that are multiples of both [latex]2[\/latex] and [latex]5[\/latex]. That is because [latex]10=2\\cdot 5[\/latex]. Likewise, since [latex]6=2\\cdot 3[\/latex], the multiples of [latex]6[\/latex] are the numbers that are multiples of both [latex]2[\/latex] and [latex]3[\/latex].<\/p>\n<p>The following video shows how to determine the first four multiples of 6.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine Multiples of a Given Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/mkEWqspRVKk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Use Common Divisibility Tests<\/h3>\n<p>Another way to say that [latex]375[\/latex] is a multiple of [latex]5[\/latex] is to say that [latex]375[\/latex] is divisible by [latex]5[\/latex]. In fact, [latex]375\\div 5[\/latex] is [latex]75[\/latex], so [latex]375[\/latex] is [latex]5\\cdot 75[\/latex]. Notice in the last example\u00a0that [latex]10,519[\/latex] is not a multiple [latex]3[\/latex]. When we divided [latex]10,519[\/latex] by [latex]3[\/latex] we did not get a counting number, so [latex]10,519[\/latex] is not divisible by [latex]3[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>Divisibility<\/h3>\n<p>If a number [latex]m[\/latex] is a multiple of [latex]n[\/latex], then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex].<\/p>\n<\/div>\n<p>Since multiplication and division are inverse operations, the patterns of multiples that we found can be used as divisibility tests. The table below\u00a0summarizes divisibility tests for some of the counting numbers between one and ten.<\/p>\n<table id=\"fs-id2134771\" style=\"width: 85%;\" summary=\"This table has five rows and two columns. The first row is a header row that labels each column. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"2\"><strong>Divisibility Tests<\/strong><\/th>\n<\/tr>\n<tr valign=\"top\">\n<th><strong>A number is divisible by<\/strong><\/th>\n<th><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]2[\/latex]<\/td>\n<td>if the last digit is [latex]0,2,4,6,\\text{or }8[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]3[\/latex]<\/td>\n<td>if the sum of the digits is divisible by [latex]3[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]5[\/latex]<\/td>\n<td>if the last digit is [latex]5[\/latex] or [latex]0[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]6[\/latex]<\/td>\n<td>if divisible by both [latex]2[\/latex] and [latex]3[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10[\/latex]<\/td>\n<td>if the last digit is [latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether [latex]1,290[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q289804\">Show Solution<\/span><\/p>\n<div id=\"q289804\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe table below\u00a0applies the divisibility tests to [latex]1,290[\/latex]. In the far right column, we check the results of the divisibility tests by seeing if the quotient is a whole number.<\/p>\n<table id=\"fs-id1405269\" style=\"width: 85%;\" summary=\"This table has five rows and four columns. The first row is a header row that labels each column. The columns are labeled\">\n<thead>\n<tr valign=\"top\">\n<th><strong>Divisible by\u2026?<\/strong><\/th>\n<th><strong>Test<\/strong><\/th>\n<th><strong>Divisible?<\/strong><\/th>\n<th><strong>Check<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]2[\/latex]<\/td>\n<td>Is last digit [latex]0,2,4,6,\\text{or }8?[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]1290\\div 2=645[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\text{Is sum of digits divisible by }3?[\/latex]<\/p>\n<p>[latex]1+2+9+0=12[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]1290\\div 3=430[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]5[\/latex]<\/td>\n<td>Is last digit [latex]5[\/latex] or [latex]0?[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]1290\\div 5=258[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10[\/latex]<\/td>\n<td>Is last digit [latex]0?[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]1290\\div 10=129[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Thus, [latex]1,290[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom5\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145433&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether [latex]5,625[\/latex] is divisible by [latex]2,3,5,\\text{and }10[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q246871\">Show Solution<\/span><\/p>\n<div id=\"q246871\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe table below\u00a0applies the divisibility tests to [latex]5,625[\/latex] and tests the results by finding the quotients.<\/p>\n<table id=\"fs-id1970659\" style=\"width: 85%;\" summary=\"This table has five rows and four columns. The first row is a header row that labels each column. The columns are labeled\">\n<thead>\n<tr valign=\"top\">\n<th><strong>Divisible by\u2026?<\/strong><\/th>\n<th><strong>Test<\/strong><\/th>\n<th><strong>Divisible?<\/strong><\/th>\n<th><strong>Check<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]2[\/latex]<\/td>\n<td>Is last digit [latex]0,2,4,6,\\text{or }8?[\/latex] <em>No.<\/em><\/td>\n<td>no<\/td>\n<td>[latex]5625\\div 2=2812.5[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]\\text{Is sum of digits divisible by }3?[\/latex]<\/p>\n<p>[latex]5+6+2+5=18[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]5625\\div 3=1875[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]5[\/latex]<\/td>\n<td>Is last digit is [latex]5[\/latex] or [latex]0?[\/latex] <em>Yes.<\/em><\/td>\n<td>yes<\/td>\n<td>[latex]5625\\div 5=1125[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10[\/latex]<\/td>\n<td>Is last digit [latex]0?[\/latex] <em>No.<\/em><\/td>\n<td>no<\/td>\n<td>[latex]5625\\div 10=562.5[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Thus, [latex]5,625[\/latex] is divisible by [latex]3[\/latex] and [latex]5[\/latex], but not [latex]2[\/latex], or [latex]10[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145433\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145433&theme=oea&iframe_resize_id=ohm145433&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video lesson shows how to determine whether a number is divisible by [latex]2,3,4,5,6,8,9,10[\/latex]<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Divisibility Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/i16N01IdIhk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9436\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 145433, 145363, 145413, 145417, 145418. <strong>Authored by<\/strong>: Lumen Learnig. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>:  IMathAS Community License<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Determine Multiples of a Given Number. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/mkEWqspRVKk\">https:\/\/youtu.be\/mkEWqspRVKk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Divisibility Rules. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/i16N01IdIhk\">https:\/\/youtu.be\/i16N01IdIhk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17535,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Determine Multiples of a Given Number\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/mkEWqspRVKk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Divisibility Rules\",\"author\":\"James Sousa 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License\"}]","CANDELA_OUTCOMES_GUID":"c89ddcc8-7c26-43a2-a2b2-1a900740afa2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9436","chapter","type-chapter","status-publish","hentry"],"part":16105,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17535"}],"version-history":[{"count":21,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9436\/revisions"}],"predecessor-version":[{"id":16110,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9436\/revisions\/16110"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/16105"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9436\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=9436"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9436"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=9436"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=9436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}