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Chapter Overview

Learning Goals

Maths

Common factors and multiples

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Summary

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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.

Common factors and multiples

In a nutshell

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.

Want to find out more? Check out these other lessons!

Multiples and factors

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Frequently Asked Questions (FAQ)

FAQs

Question: What are common factors?

Answer: Common factors are factors of two or more numbers which are the same.
Question: What is a common multiple?

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

Theory

Exercises

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Common factors and multiples

Common factors and multiples

In a nutshell

Common multiples

Example 1

Multiples of $\bold6$

Multiples of $\bold9$

Common factors

Example 2

Common factors and multiples

In a nutshell

Common multiples

Example 1

Multiples of $\bold6$

Multiples of $\bold9$

Common factors

Example 2

Want to find out more? Check out these other lessons!

Frequently Asked Questions (FAQ)

Theory understood?

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Common factors and multiples

​Common factors and multiples

​​In a nutshell

Common multiples

Example 1

Multiples of 6\bold66​

Multiples of 9\bold99​

Common factors

Example 2

​Common factors and multiples

​​In a nutshell

Common multiples

Example 1

Multiples of 6\bold66​

Multiples of 9\bold99​

Common factors

Example 2

Want to find out more? Check out these other lessons!

Theory understood?

Common factors and multiples

In a nutshell

Multiples of $\bold6$

Multiples of $\bold9$

Common factors and multiples

In a nutshell

Multiples of $\bold6$

Multiples of $\bold9$