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

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

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Summary

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

​​In a nutshell

Counting in multiples of 6,76,7 and 99 is similar to recalling timetables. There are tricks and patterns that can be used make multiples easier remember - in particular for 2525 and 1 0001\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 66, create a sequence and add six to each number, starting from zero.

0+66+612+618+6240 \xrightarrow[]{+6} \underline6 \xrightarrow[]{+6} \underline{12}\xrightarrow[]{+6} \underline{18}\xrightarrow[]{+6}\underline{24}


All the multiples of 66 up to 7272 are listed below.

6,12,18,24,30,36,42,48,54,60,66,726,12,18,24,30,36,42,48,54,60,66,72


Patterns to notice about multiples of 66​:

  • They are all even: each multiple of 66 ends in 2,4,6,82,4,6,8 or 00.
  • Their final digits follow the pattern 6,2,8,4,06,2,8,4,0​.


Multiples of 7

Multiples of 77 are an extension of the seven times tables. To find the multiples of 77, create a sequence and add seven to each number, starting from zero.

0+77+714+721+7280 \xrightarrow[]{+7} \underline7 \xrightarrow[]{+7} \underline{14}\xrightarrow[]{+7} \underline{21}\xrightarrow[]{+7}\underline{28}


All the multiples of 77​ up to 8484 are listed below.

7,14,21,28,35,42,49,56,63,70,77,847,14,21,28,35,42,49,56,63,70,77,84


Note: Multiples of 77 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 99, 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.

01+1091+10181+10271+10360 \xrightarrow[-1]{+10} \underline{9} \xrightarrow[-1]{+10} \underline{18}\xrightarrow[-1]{+10} \underline{27}\xrightarrow[-1]{+10}\underline{36}

All the multiples of 99​ up to 108108 are listed below.

9,18,27,36,49,54,63,72,81,90,99,1089,18,27,36,49,54,63,72,81,90,99,108


Patterns to notice about multiples of 99​:

  • 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 90.90.​ 

​​Example

Is 198198 a multiple of 99?


Add up the digits.

1+9+8=181+8=91+9+8=18\\1+8=9


The digits add up to nine so yes.

​​

Multiples of 25

To find the multiples of 2525create a sequence and add 2525 to each number, starting from zero. An easy way to do this is to add twenty and then add five. 

0+5+2025+5+2050+5+2075+5+201000 \xrightarrow[+5]{+20} \underline{25} \xrightarrow[+5]{+20} \underline{50}\xrightarrow[+5]{+20} \underline{75}\xrightarrow[+5]{+20}\underline{100}​​


All the multiples of 2525​ up to 250250 are listed below.

25,50,75,100,125,150,175,200,225,25025,50,75,100,125,150,175,200,225,250


Patterns to notice about multiples of 2525​:

  • They all end in either 00,25,5000,25,50 or 7575.
  • They are all multiples of five: each multiple of 2525 ends in 55 or 00.
  • Each multiple of 2525 is half of a multiple of 5050.​

Multiples of 1000

Counting in multiples of 1 0001\thinspace 000 is very similar to counting in multiples of 1010, except there are an extra two zeros on the end.


Multiples of 1010:

0+1010+1020+1030+10400 \xrightarrow[]{+10} \underline{10} \xrightarrow[]{+10} \underline{20}\xrightarrow[]{+10} \underline{30}\xrightarrow[]{+10}\underline{40}


Multiples of 1 0001\thinspace 000

0+10001 000+10002 000+10003 000+10004 0000 \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 0001\thinspace 000 is one hundred lots of 1010.


All the multiples of 1 0001\thinspace 000​ up to 10,00010,000 are listed below.

1 000,2 000,3 000,4 000,5 000,6 000,7 000,8 000,9 000,10 0001\thinspace000,2\thinspace000,3\thinspace000,4\thinspace000,5\thinspace000,6\thinspace000,7\thinspace000,8\thinspace000,9\thinspace000,10\thinspace000


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FAQs - Frequently Asked Questions

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