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Divisibility rules

You learn rules to check if a number divides by 2, 3, 4, 5, 6, 8, 9 or 10.

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How to work it out

  1. Divisible by 3 or 9: add up the digits (is the sum divisible by 3 or 9?).
  2. Divisible by 5: ends in 0 or 5.
  3. Divisible by 2: even number.
3 × 8

A worked example

Is 248 divisible by 2?

  1. Check the last digit: 8 is even.
  2. So 248 is divisible by 2.
More examples

Is 315 divisible by 3?

  1. Add the digits: 3 + 1 + 5 = 9.
  2. 9 is divisible by 3.
  3. So 315 is divisible by 3.

Is 240 divisible by 5?

  1. The last digit is 0.
  2. Numbers ending in 0 or 5 are divisible by 5.
  3. So 240 is.

Try it yourself

  1. Answer with yes or no

    Is 526 divisible by 3?

  2. Answer with yes or no

    Is 518 divisible by 4?

Watch out

  • For 3 you only look at the last digit, and then you choose wrongly.

    Only for 2, 5 and 10 does the last digit count. For 3 and 9 you add up all the digits.

  • You think 12 is divisible by 9 because 12 is divisible by 3.

    For 9 the sum of the digits must be in the 9 times table: 9, 18, 27. For 3, 12 is enough.

Tips

  • Divisible by 2: last digit is even
  • Divisible by 5: last digit is 0 or 5
  • Divisible by 10: last digit is 0
  • Divisible by 3: sum of digits is divisible by 3
  • Divisible by 9: sum of digits is divisible by 9

Why it works

With these rules you can quickly check whether a number is divisible. You do not have to work out the whole sum.