Factors And Multiples

 

Factors and multiples are different. But they both involve multiplication:

  • Factors are what we can multiply to get the number
  • Multiples are what we get after multiplying the number by an integer

Demonstration:

A number can have many factors.

3 × 6 = 18, so 3 and 6 are factors of 18

Also 2 × 9 = 18, so 2 and 9 are also factors of 18,

And 1 × 18 = 18, so 1 and 18 are factors of 18 as well.

And because multiplying negatives makes a positive, −1, −2, −3, −6, −9 and −18 are also factors of 18:

(−1) × (−18) = 18

(−2) × (−9) = 18

(−3) × (−6) = 18

So all the factors of 18 are:

1, 2, 3, 6, 9 and 18  And −1, −2, −3, −6, −9 and −18

A multiple is the result of multiplying a number by an Integer

Example: 14 is a multiple of 2, as 2 × 7 = 14 
Example: 16 is not a multiple of 3

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