Summary: Finding Multiples and Factors

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.
    1. Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
      1. If the quotient is a counting number, the divisor and quotient are a pair of factors.
      2. If the quotient is not a counting number, the divisor is not a factor.
    2. List all the factor pairs.
    3. Write all the factors in order from smallest to largest.
  • Determine if a number is prime.
    1. Test each of the primes, in order, to see if it is a factor of the number.
    2. Start with [latex]2[/latex] and stop when the quotient is smaller than the divisor or when a prime factor is found.
    3. If the number has a prime factor, then it is a composite number. If it has no prime factors, then the number is prime.