## Dictionary Definition

The Oxford English Dictionary defines a factor as "each of two or more whole numbers or quantities which, when multiplied together, produce a given number or expression."## A Real Example of Factors

It is easier to understand factors with an example. If we multiply**2**and

**5**together, the answer is 10.

**2**and

**5**are

**factors**of 10.

If we multiply

**1**and

**10**together, the answer is 10.

**1**and

**10**are also

**factors**of 10.

The factors of 10 are:

## Dividing by Factors

We have seen that**1**,

**2**,

**5**and

**10**are factors of 10. All of these numbers divide exactly into 10:

10 ÷ **1** = 10

10 ÷ **2** = 5

10 ÷ **5** = 2

10 ÷ **10** = 1

**Note:**When we divide a number by one of its factors, the answer is another factor.

## More Real Examples of Factors

- The factors of
**6**are the numbers that multiply together to make 6.**1**×**6**= 6**2**×**3**= 6

- The factors of
**18**are the numbers that multiply together to make 18.**1**×**18**= 18**2**×**9**= 18**3**×**6**= 18

- The factors of
**48**are the numbers that multiply together to make 48.**1**×**48**= 48**2**×**24**= 48**3**×**16**= 48**4**×**12**= 48**6**×**8**= 48

## Factor, Factorisation

To write a number or term as a product of its factors is called 'to factor' or 'to factorise'. For example, to factor (or factorise) 10, we can write:1 × 10 = 10

2 × 5 = 10

## Factors, Prime and Composite Numbers

- If the only factors of a number are 1 and itself, then the number is a prime number. For example, 5 is a prime number because its only factors are 1 and 5.
- If a number has at least one factor other than 1 and itself, it is a composite number. For example, 6 is a composite number as its factors are 1, 2, 3 and 6.

## Factors in Algebra

Just as numbers have factors, terms in algebra also have factors. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term. For example, the factors of**2**and

**x**are factors of

**2x**, because

**2**×

**x**=

**2x**. Learn more about factors in algebra

## You might also like...

numbersunderstanding long division with decimalsfinding factorsunderstanding the greatest common factor

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.