Factors are numbers which, when multiplied together, produce the desired result.

For example 2 and 6 are factors of the number 12, because 2 and 6, when multiplied together produce the desired 12.

Some numbers have many factors for example 12:

2 , 6 because 2 × 6 = 12
3 , 4 because 3 × 4 = 12
2, 2, 3 because 2×2×3 = 12

One and the number itself don't count

We don't usually think of the number one and the number itself as factors.
For example 1 × 12 = 12.
This is because any number can always be factored this way

Prime numbers have no factors

The definition of a prime number is one with no factors (except 1 and itself). See Prime number.


Factoring is the act of finding the factors of a number. With large numbers it can be surprisingly difficult to do. Some encryption system work by multiplying together two known large prime numbers and using it to scramble text. This works because the reverse process of finding the two prime factors of a number is extremely difficult to do - even with supercomputers.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values