# How to factor

## What is a factor?

A factor of a number divides that number. It can be multiplied by another factor to equal the target number.

For example, the factors of 12 are:

1, 2, 3, 4, 6, & 12

By definition, you can multiply any of these factors by some other factor to equal 12.

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

The numbers on the left are all the factors of 12.

## Every number has at least 2 factors

This may be obvious, but each number can be divided by 1 and itself.

If we wanted to find all of the factors of 12, we could start with 12 and 1.

## From 2 to n / 2 test each number to see if it is a factor

To find the factors of 12, we already know that 1 and 12 are factors.

Next, we know that (besides 12) no number higher than 6 (12 / 2) can be a factor. So we can start at 2 and test each number up to 6 to see if is a factor of 12.

2) 12 / 2 = 6 yes

3) 12 / 3 = 4 yes

4) 12 / 4 = 3 yes

5) 12 / 5 = 2.4 no

6) 12 / 6 = 2 yes

So to 1 and 12 we can add 2, 3, 4 and 6.