### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Factors

Factors of a number are the numbers that exactly divide that number, leaving no remainders. Let’s look at how to find the factors of a given number.

For example, the factors of are and . The factors of are and , since the division of by either or results in whole numbers.

## Finding Factors of Larger Numbers

With larger numbers, we have to be careful when finding the factors, as we can easily make mistakes like missing a factor or including numbers which are not factors. Let’s look at an example.

### Example

Find the factors of .

To find the factors of , we can create a table like the one below:

1. Start with the smallest factor, which is always . Write in the left column and in the right column, since .

2. Check each integer in ascending order to see if it is a factor. If it is, write the factor in the left column and the result of the division in the right column.

3. Continue this process until a factor repeats itself. In this case, we stop after writing and , since is already in the right column.

Now, we can list down the factors of :

Start from the left-hand column, starting from , and make your way down: and . After this, move to the right-hand column, and make your way up: and .

Therefore, the factors of are: and .