2.4 Find multiples and factors  (Page 5/9)

Key concepts

• 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.

Practice makes perfect

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,3,4,5,6,\text{and}10.$

Find All the Factors of a Number

In the following exercises, find all the factors of the given number.

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

Everyday math

Writing exercises

Self check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?