Tag: proof of divisibility

Divisibility Rules

A number is divisible by 2 if…

it ends in 0, 2, 4, 6 or 8

e.g. 10, 2002, 1008…

A number is divisible by 3 if…

the sum of its digits is a multiple of 3

e.g. 1002 (1 + 0 +0 + 2 = 3 and 3 is a multiple of 3), 31008 (the digits add up to 12 and 12 is a multiple of 3)

A number is divisible by 4 if…

the last two digits are a multiple of 4

e.g. 10020 (the last two digits are 2 and 0. Twenty is a multiple of 4), 61008 (08, or eight, is a multiple of 4)

A number is divisible by 7 if…

Okay, this one is a bit confusing. Take the last digit and double it. Subtract this number from the remaining digits. If you get 0 or a number divisible by 7, the original number is divisible by 7.

e.g. 1008 (double 8 is 16. 100 – 16 = 84. 84 is divisible by 7, so 1008 is too), 203 (double 3 is 6. 20 – 6 = 14. 14 is divisible by 7, so 203 is too)

A number is divisible by 10 if…

it ends in 0

e.g. 100, 20, 250…

Try writing a really long random number (at least 5 digits!) and check if it’s divisible by each number from 1 to 10.

Tell us your results in the comments below!

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