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# Summary: Finding Multiples and Factors

## Key Concepts

Divisibility Tests
A number is divisible by
$2$ if the last digit is $0, 2, 4, 6,$ or $8$
$3$ if the sum of the digits is divisible by $3$
$5$ if the last digit is $5$ or $0$
$6$ if divisible by both $2$ and $3$
$10$ if the last digit is $0$
• Factors If $a\cdot b=m$ , then $a$ and $b$ are factors of $m$ , and $m$ is the product of $a$ and $b$ .
• 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 $2$ 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.

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