Divisibility testing

Here are ways to see if an integer is divisible by:

  1. It always is.
  2. If it’s even (ends in 2,4,6,8,0) (eg. 302 ends in 2).
  3. If its digits add up to a number divisible by 3 (eg. 246 is 2+4+6=12 which is 1+2=3).
  4. If the last 2 digits of the number are an odd number, then a 2 or 6 OR an even number, then a 4 or 8 (eg. 128432 is because 32 is an odd  number, then a 2).
  5. If it ends in 5 or 0 (eg. 305).
  6. If it satisfies tests for 2 and 3 (so it’s even and it’s divisible by 3) (eg. 672 ends in 2 and 6+7+2=15 which is divisible by 3).
  7. If you double the last digit and subtract it from the rest of the number and the answer is divisible by 7 or 0 (eg. 672:  67-4=63, and 6-6=0)
  8. Look at the last 3 digits: If the hundreds digit is even, then just look at the last 2 digits to see if they are divisible by eight. If the hundreds digit is odd, see if the last two digits +4 are divisible by eight (eg. 125544 is 544, 48 is divisible by 8).
  9. If its digits add up to a number divisible by 9 (Similar to the test for 3) (eg. 117 is 1+1+7=9).
  10. If it ends in 0 (eg.2430 ends in 0).


Hello and welcome to my maths blog. I will use images (stuff like


) because I can’t use LaTex. I will post anything that I find interesting or just need to remember. I hope you find this useful.