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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 921 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 10225 divisible by 5?
  2. 2.Is 73413 divisible by 11?
  3. 3.Is 88368 divisible by 17?
  4. 4.Is 666 divisible by 9?
  5. 5.Is 33384 divisible by 13?
  6. 6.Is 86015 divisible by 17?
  7. 7.Is 42490 divisible by 8?
  8. 8.Is 14134 divisible by 7?
  9. 9.Is 15532 divisible by 11?
  10. 10.Is 16524 divisible by 18?
  11. 11.Is 41955 divisible by 7?
  12. 12.Is 39097 divisible by 24?
  13. 13.Is 112280 divisible by 24?
  14. 14.Is 82605 divisible by 24?
  15. 15.Is 55187 divisible by 29?
  16. 16.Is 4250 divisible by 5?
  17. 17.Is 115607 divisible by 29?
  18. 18.Is 8528 divisible by 13?
  19. 19.Is 82194 divisible by 19?
  20. 20.Is 17769 divisible by 18?
  21. 21.Is 38173 divisible by 20?
  22. 22.Is 95310 divisible by 15?
  23. 23.Is 71328 divisible by 23?
  24. 24.Is 19143 divisible by 9?
  25. 25.Is 3141 divisible by 8?
  26. 26.Is 21942 divisible by 5?
  27. 27.Is 9473 divisible by 5?
  28. 28.Is 28061 divisible by 11?
  29. 29.Is 5020 divisible by 2?
  30. 30.Is 17772 divisible by 6?
  31. 31.Is 19165 divisible by 12?
  32. 32.Is 48277 divisible by 23?
  33. 33.Is 69839 divisible by 11?
  34. 34.Is 22334 divisible by 13?
  35. 35.Is 10134 divisible by 9?
  36. 36.Is 28270 divisible by 6?
  37. 37.Is 79881 divisible by 19?
  38. 38.Is 90376 divisible by 18?
  39. 39.Is 48670 divisible by 11?
  40. 40.Is 149650 divisible by 24?

Answer key

  1. yes
  2. no
  3. no
  4. yes
  5. yes
  6. no
  7. no
  8. no
  9. yes
  10. yes
  11. no
  12. no
  13. no
  14. no
  15. yes
  16. yes
  17. no
  18. yes
  19. yes
  20. no
  21. no
  22. yes
  23. no
  24. yes
  25. no
  26. no
  27. no
  28. yes
  29. yes
  30. yes
  31. no
  32. yes
  33. yes
  34. yes
  35. yes
  36. no
  37. no
  38. no
  39. no
  40. no

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