Common factors and multiples

In a nutshell

A multiple is a number you get when you multiply a certain number by a whole number. A factor is a number that divides into a certain number exactly with no remainder. Multiples and factors can be shared between different numbers.

Common multiples

Common multiples are multiples which are the same between two or more numbers.

Example 1

What are all the common multiples of $6$ and $9$ between $1$ and $50$ ?

List all the multiples of $6$  and $9$  between $1$  and $50$ .

Multiples of $\bold6$	Multiples of $\bold9$
$6$	$9$
$12$	$\bold{18}$
$\bold{18}$	$27$
$24$	$\bold{36}$
$30$	$45$
$\bold{36}$
$42$
$48$

Identify the common multiples in the table.

Common multiples of $6$ and $9$ are $\underline{18,36}$ .

Note: There are an infinite number of common multiples between all numbers.

Common factors

Common factors are factors of two or more numbers which are the same.

Example 2

What are the common factors of $24$ and $16$ ?

Identify the factors of $24$ .

Factors of $24$ are $1,2,3,4,6,8,12,24$ 

Identify the factors of $16$ .

Factors of $16$ are $1,2,4,8,16$ 

Identify which factors are the same for $24$  and $16$ .

Common factors of $16$ and $24$ are $\underline{1,2,4,8}$ .

Note: By listing factors it is possible to find the highest common factor between numbers.