Factors and Multiples

Factors and multiples are both to do with multiplication:

  • Factors are what we can multiply to get the number
  • Multiples are what we get after multiplying the number by an integer (not a fraction).

Here are the details:

Factors

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

factors

2 and 3 are factors of 6

A number can have many factors.

Example: 12

  • 3 × 4 = 12, so 3 and 4 are factors of 12
  • Also 2 × 6 = 12, so 2 and 6 are also factors of 12,
  • And 1 × 12 = 12, so 1 and 12 are factors of 12 as well.

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

  • (−1) × (−12) = 12
  • (−2) × (−6) = 12
  • (−3) × (−4) = 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:

..., −9, −6, −3, 0, 3, 6, 9, ...

So we know that 12 is a multiple of 3, as 3 × 4 = 12

But 7 is NOT a multiple of 3

Multiple

Example: Multiples of 5:

..., −15, −10, −5, 0, 5, 10, 15, ...

So we know that 30 is a multiple of 5, as 5 × 6 = 30

But 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, ...