Pre-Algebra · Quick Reference

Factors & Multiples Cheat Sheet

Pre-Algebra · Lesson 7/10

In one line: factors and multiples describe two related but opposite ideas — what divides evenly into a number, and what a number divides evenly into.

Key Ideas

1Factor. A number that divides another number exactly, with no remainder. Example: 3 is a factor of 12, since 12/3=4 exactly.

2Multiple. The result of multiplying a number by any whole number. Example: 12 is a multiple of 3, since 3x4=12.

3Finding All Factors. To find every factor of a number, test each whole number up to its square root and pair it with its corresponding co-factor.

4Finding Multiples. To list multiples of a number, multiply it by 1, 2, 3, 4, and so on.

5Factor Pairs. Two numbers that multiply together to give a specific product, such as 3 and 4 being a factor pair of 12.

Worked Examples

Find all factors of 18.

Factors of 18: 1, 2, 3, 6, 9, 18

List the first 5 multiples of 7.

7, 14, 21, 28, 35

Is 6 a factor of 42?

Yes, 6 is a factor of 42

Practice Yourself

Find all factors of 20.

1, 2, 4, 5, 10, 20

List the first 5 multiples of 4.

4, 8, 12, 16, 20

Is 9 a factor of 45?

Yes, 45/9=5

Is 7 a factor of 50?

No, 50/7 is not a whole number