​​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 $$5$$?

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

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

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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  $$8$$.

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

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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 $$2$$.​