Understanding Factors and Multiples

In math, factors and multiples are two important ways to think about how numbers relate to each other through multiplication and division.

What are Factors?

A factor is a number that divides exactly into another number with no remainder. When you multiply two whole numbers together to get a product, both of those numbers are factors of the product.

We often find factors in factor pairs. Let's find all the factor pairs for the number $36$:

• $1 \times 36 = 36$
• $2 \times 18 = 36$
• $3 \times 12 = 36$
• $4 \times 9 = 36$
• $6 \times 6 = 36$

So, the factor pairs of $36$ are $(1, 36)$, $(2, 18)$, $(3, 12)$, $(4, 9)$, and $(6, 6)$. The complete list of individual factors for $36$ is $1, 2, 3, 4, 6, 9, 12, 18,$ and $36$.

What are Multiples?

A multiple is the result of multiplying a given number by another whole number. An easy way to think about multiples is simply "skip counting" by that number.

For example, what are the first five multiples of $7$? We find them by multiplying $7$ by $1, 2, 3, 4,$ and $5$:

$7 \times 1 = 7$ $7 \times 2 = 14$ $7 \times 3 = 21$ $7 \times 4 = 28$ $7 \times 5 = 35$

The first five multiples of $7$ are $7, 14, 21, 28,$ and $35$.

How to Tell if a Number is a Multiple

To check if a larger number is a multiple of a smaller number, you can use division. If the smaller number divides into the larger number with no remainder, it is a multiple.

Example: Is $56$ a multiple of $8$?

Divide $56$ by $8$: $56 \div 8 = 7$

Because $8$ goes into $56$ exactly $7$ times with no remainder, yes, $56$ is a multiple of $8$.