# 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.*