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Divisibility Test

Practise using the quick ways to spot whether a number is divisible by the digits 2 to 9.

Exercise What are the divisibility tests? Activities with Factors More Number Patterns

Tick boxes to show where the black number is exactly divisible by the red number.

23456789
24 Correct Wrong
26 Correct Wrong
36 Correct Wrong
46 Correct Wrong
99 Correct Wrong
227 Correct Wrong
29353 Correct Wrong
36821 Correct Wrong
46126 Correct Wrong
6307970 Correct Wrong

If you are confident with this concept try the Delightfully Divisible challenge.

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Featured Activity

Remainder Race

Remainder Race

A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.

Answers

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Divisibility Tests:

A number is divisible by 2 if its last digit is even (0,2,4,6 or 8)

A number is divisible by 3 if the sum of its digits is divisible by 3.

A number is divisible by 4 if the number's last two digits are divisible by 4.

A number is divisible by 5 if its last digit is a 0 or 5.

A number is divisible by 6 if it is divisible by 2 and 3 (see rules above).

A number is divisible by 7 if 5 times the last digit added to the number made from the other digits is divisible by 7.

A number is divisible by 8 if the last three digits form a number that is divisible 8.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if its last digit is 0.

A number is divisible by 11 if the alternating sum of its digits is divisible by 11. Alternating sum means a-b+c-d+... – m

A number is divisible by 12 if it is divisible by 3 and 4.

 

The projectable version of the divisibility tests can be found here: Divisibility Tests 2-12

There is a printable worksheet to go with this activity.

Worksheet

The divisibility test for 7 is thanks to a 12-year old pupil, Chika Ofili, from Westminster School. You can read more about it here.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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