# Multiples and factors

## 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

Multiples are the numbers you get by multiplying a certain number by a whole number. The times table displays the multiples of different numbers.

##### Example 1

*What are the first *$10$* multiples of* $5$*?*

$\begin{aligned} 5 \times 1 &=5 \\ 5 \times 2 &= 10 \\ 5 \times 3 &= 15 \\5 \times 4 &= 20 \\5 \times 5 &= 25 \\5 \times 6 &= 30 \\5 \times 7 &= 35 \\5 \times 8 &= 40 \\5 \times 9 &= 45 \\ 5 \times 10 &= 5 0\\\end{aligned}$

$\underline{Multiples\space of\space 5 = 5,10,15,20,25,30,35,40,45,50.}$

## Factors

Factors are numbers that divide into a certain number exactly with no remainder. Factors always come in pairs.

##### Example 2

*What are the factors of* $30$?

$\begin{aligned} &1 \times 30 &= 30 \\ &2 \times 15 &= 30 \\ &3 \times 10 &= 30 \\ &5 \times 6 &= 30 \end{aligned}$

$\underline{Factors\space of\space30=1,2,3,5,6,10,15,30.}$

**Note:** *All numbers are a factor of themselves and $1$. *

## Common factors

A common factor is a factor of two or more numbers which is the same.

##### Example 3

*What are the common factors of $20$ and $8$?*

*Identify the factors of $20$.*

*${Factors\space of\space20=1,2,4,5,10,20}$*

*Identify the factors of *$8$.

${Factors\space of\space8=1,2,4,8}$

*Identify which factors are the same for *$8$* and *$20$*. *

$\underline{Factors\space of\space8 \space and\space 20 =1,2,4.}$

*Note:** All even numbers have a common factor of *$2$**.**