Factors and Multiples

Factors and multiples are both to do with multiplication:

  • Factors are what you can multiply to get a number
  • Multiples are what you get after multiplying a number by an integer.

Here are the details:

Factors

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

factors

2 and 3 are factors of 6

A number can have many factors.

Example: 3 and 4 are factors of 12, because 3×4=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
Like this: (-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).

Examples:

Multiple

Multiples of 3:

12 is a multiple of 3, because 3 × 4 = 12

-3 is a multiple of 3, because 3 × -1 = -3

 

Multiples of 5:

10 is a multiple of 5, because 5 × 2 = 10

But 11 is NOT a multiple of 5

So you 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, ...

Learn more about Least Common Multiple.