Divisibility rules OK!


And, no, this is nothing to do with Harry Potter’s invisibility cloak…

Times tables can be tricky, and there’s no substitute for learning them by heart. However, the divisibility rules can at least tell you whether an answer is definitely wrong. I’m a great believer in ‘sanity checking’ your work. Just ask yourself, “Is this crazy?” If it is, you’ll have to do the question again!

The divisibility rules are quite simple (except for the ones for 7 and 8). They tell you whether a number can be divided by any number from 1 to 10. They’re most useful when simplifying fractions…or when you’re struggling to remember your times tables!

  1. Must be a whole number, eg 2, but not 2.5.
  2. Must be an even number ending in 0, 2, 4, 6 or 8, eg 22, but not 23.
  3. The sum of the digits must be divisible by 3, eg 66, but not 67.
  4. The number formed by the last two digits must be ’00’ or divisible by 8, eg 500 or 504, but not 503.
  5. Must end in 5 or 0, eg 60, but not 61.
  6. Must be divisible by both 2 and 3, eg 18, but not 23.
  7. If you double the last digit and take this away from the number formed by the rest of the digits, the result must be 0 or divisible by 7, eg 672 (2 x 2 = 4, and 67 – 4 = 63, which is divisible by 7), but not 674.
  8. The number formed by the last three digits must be ’00’ or divisible by 8, eg 5,000 or 5,008, but not 5,003.
  9. The sum of the digits must be divisible by 9, eg 666, but not 667.
  10. Must end in 0, eg 110, but not 111.
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