Factors and Multiples

Factors and multiples are different things.

But they both involve multiplication:

Example: the positive factors, and some multiples, of 6:

factors of 6: ...,1,2,3,6; multiples of 6: ... 0, 6, 12, 18, ...

Factors:

Multiples:

(Note: there are negative factors and multiples as well)

Here are the details:

Factors

"Factors" are the numbers we can multiply together to get another number:

in 2x3=6, 2 and 3 are factors

2 and 3 are factors of 6

A number can have many factors.

Example: 12

AND because multiplying negatives makes a positive, −1, −2, −3, −4, −6 and −12 are also factors of 12:

So ALL the factors of 12 are:

1, 2, 3, 4, 6 and 12
AND −1, −2, −3, −4, −6 and −12

Learn about Greatest Common Factor and how to find All Factors of a Number.

Multiples

A multiple is the result of multiplying a number by an integer (not a fraction).

Example: Multiples of 3:

Multiples of 3: ..., −9, −6, −3, 0, 3, 6, 9, ...
..., −9, −6, −3, 0, 3, 6, 9, ...

Example: 15 is a multiple of 3, as 3 × 5 = 15
Example: 16 is not a multiple of 3

Example: Multiples of 5:

Multiples of 5: ..., −15, −10, −5, 0, 5, 10, 15, ...
..., −15, −10, −5, 0, 5, 10, 15, ...

Example: 10 is a multiple of 5, as 5 × 2 = 10
Example: 11 is not a multiple of 5

Learn more about Least Common Multiple.

Multiples of Anything

We must multiply by an integer, but the number that is being multiplied can be anything.

Example: Multiples of π

..., −2π, −π, 0, π, 2π, 3π, 4π, ...