Key Concepts
Divisibility Tests | |
---|---|
A number is divisible by | |
[latex]2[/latex] | if the last digit is [latex]0, 2, 4, 6,[/latex] or [latex]8[/latex] |
[latex]3[/latex] | if the sum of the digits is divisible by [latex]3[/latex] |
[latex]5[/latex] | if the last digit is [latex]5[/latex] or [latex]0[/latex] |
[latex]6[/latex] | if divisible by both [latex]2[/latex] and [latex]3[/latex] |
[latex]10[/latex] | if the last digit is [latex]0[/latex] |
- Factors If [latex]a\cdot b=m[/latex] , then [latex]a[/latex] and [latex]b[/latex] are factors of [latex]m[/latex] , and [latex]m[/latex] is the product of [latex]a[/latex] and [latex]b[/latex] .
- Find all the factors of a counting number.
- Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
- If the quotient is a counting number, the divisor and quotient are a pair of factors.
- If the quotient is not a counting number, the divisor is not a factor.
- List all the factor pairs.
- Write all the factors in order from smallest to largest.
- Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
- Determine if a number is prime.
- Test each of the primes, in order, to see if it is a factor of the number.
- Start with [latex]2[/latex] and stop when the quotient is smaller than the divisor or when a prime factor is found.
- If the number has a prime factor, then it is a composite number. If it has no prime factors, then the number is prime.