What Is a Factor?
What Is a Factor?
A factor is a number which divides exactly into another number.
The numbers that are multiplied together to make another number are factors.
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 6 are:

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 18 are:

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
The factors of 48 are: