# Counting in multiples of 6, 7, 9, 25 and 1000

## In a nutshell

Counting in multiples of $6,7$ and $9$ is similar to recalling timetables. There are tricks and patterns that can be used make multiples easier remember - in particular for $25$* *and* *$1\thinspace 000$*.*

## What is a multiple?

### Definition

A multiple is the result of multiplying two numbers together. Counting in multiples means starting from zero and adding the same number each time. It is the easiest way to see multiples and the patterns that they produce.

### Multiples of 6

To find the multiples of $6$, create a sequence and add six to each number, starting from zero.

$0 \xrightarrow[]{+6} \underline6 \xrightarrow[]{+6} \underline{12}\xrightarrow[]{+6} \underline{18}\xrightarrow[]{+6}\underline{24}$

All the multiples of $6$ up to $72$ are listed below.

$6,12,18,24,30,36,42,48,54,60,66,72$

Patterns to notice about multiples of $6$:

- They are all even: each multiple of $6$ ends in $2,4,6,8$ or $0$.
- Their final digits follow the pattern $6,2,8,4,0$.

### Multiples of 7

Multiples of $7$ are an extension of the seven times tables. To find the multiples of $7$, create a sequence and add seven to each number, starting from zero.

$0 \xrightarrow[]{+7} \underline7 \xrightarrow[]{+7} \underline{14}\xrightarrow[]{+7} \underline{21}\xrightarrow[]{+7}\underline{28}$

All the multiples of $7$ up to $84$ are listed below.

$7,14,21,28,35,42,49,56,63,70,77,84$

*Note**: Multiples of *$7$* can be tricky to remember as there aren't any obvious patterns to help - practise repeating them from memory! *

### Multiples of 9

To find the multiples of $9$, create a sequence and add nine to each number, starting from zero. An easy way to do this is to add ten and then take away one.

$0 \xrightarrow[-1]{+10} \underline{9} \xrightarrow[-1]{+10} \underline{18}\xrightarrow[-1]{+10} \underline{27}\xrightarrow[-1]{+10}\underline{36}$

All the multiples of $9$ up to $108$ are listed below.

$9,18,27,36,49,54,63,72,81,90,99,108$

Patterns to notice about multiples of $9$:

- Their digits add up to nine (or multiples of).
- When in order, as the tens column increases by one, the units decrease by one, up to the number $90.$

##### Example

*Is *$198$* a multiple of *$9$*?*

*Add up the digits.*

$1+9+8=18\\1+8=9$

*The digits add up to nine so *__yes.__

### Multiples of 25

To find the multiples of $25$, create a sequence and add $25$ to each number, starting from zero. An easy way to do this is to add twenty and then add five.

$0 \xrightarrow[+5]{+20} \underline{25} \xrightarrow[+5]{+20} \underline{50}\xrightarrow[+5]{+20} \underline{75}\xrightarrow[+5]{+20}\underline{100}$

All the multiples of $25$ up to $250$ are listed below.

$25,50,75,100,125,150,175,200,225,250$

Patterns to notice about multiples of $25$:

- They all end in either $00,25,50$ or $75$.
- They are all multiples of five: each multiple of $25$ ends in $5$ or $0$.
- Each multiple of $25$ is half of a multiple of $50$.

### Multiples of 1000

Counting in multiples of $1\thinspace 000$ is very similar to counting in multiples of $10$, except there are an extra two zeros on the end.

Multiples of $10$:

$0 \xrightarrow[]{+10} \underline{10} \xrightarrow[]{+10} \underline{20}\xrightarrow[]{+10} \underline{30}\xrightarrow[]{+10}\underline{40}$

Multiples of $1\thinspace 000$:

$0 \xrightarrow[]{+1000} \underline{1\thinspace 000} \xrightarrow[]{+1000} \underline{2\thinspace 000}\xrightarrow[]{+1000} \underline{3\thinspace 000}\xrightarrow[]{+1000}\underline{4\thinspace 000}$

This is because $1\thinspace 000$ is one hundred lots of $10$.

All the multiples of $1\thinspace 000$ up to $10,000$ are listed below.

$1\thinspace000,2\thinspace000,3\thinspace000,4\thinspace000,5\thinspace000,6\thinspace000,7\thinspace000,8\thinspace000,9\thinspace000,10\thinspace000$