A factor is a number which divides exactly into another number.
The numbers that are multiplied together to make another number are factors.

If we multiply

The factors of 10 are:

The method is refered to as 'factoring' or 'factorising'.
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## 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

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