Home > Pre-Algebra > Factors and Multiples > Listing Factors

## Listing Factors

#### Introduction

#### Terms

**Factor**- A number that evenly divides into another without leaving a remainder.

## Lesson

When we are asked to list all the factors of a number, we are being asked to simply list all the numbers that can evenly divide (i.e. leave no remainder) into the given number. So if we are given 25, we first determine all the factors of 25:

$1 * 25 = 25$

$5 * 5 = 25$

$25 * 1 = 25$

And then we just list them as the answer: 1, 5, 25.

Note that the 5 only gets listed once!

Similarly, when asked to list the factors for 44, we get:

$1*44=44$

$2*22=44$

$4*11=44$

$11*4=44$

$22*2=44$

$44*1=44$

So the factors of 44 are $1, 2, 4, 11, 22, 44$

## Examples

#### Listing Factors (Example #1)

$24$

We need to find all whole number pairs whose product is 24

$1 * 24 = 24$

$2 * 12 = 24$

$3 * 8 = 24$

$4 * 6 = 24$

The factors of $24$ are $1, 2, 3, 4, 6, 8, 12\text{ and }24$

#### Listing Factors (Example #2)

$29$

We need to find all whole number pairs whose product is 29

$1 * 29 = 29$

The factors of $29$ are $1\text{ and }29$

#### Listing Factors (Example #3)

$32$

We need to find all whole number pairs whose product is 32

$1 * 32 = 32$

$2 * 16 = 32$

$4 * 8 = 32$

The factors of $32$ are $1, 2, 4, 8, 16\text{ and }32$

#### Listing Factors (Example #4)

$64$

We need to find all whole number pairs whose product is 64

$1 * 64 = 64$

$2 * 32 = 64$

$4 * 16 = 64$

The factors of $64$ are $1, 2, 4, 8, 16, 32\text{ and }64$