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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.