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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 991 · 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 63921 divisible by 13?
  2. 2.Is 120683 divisible by 20?
  3. 3.Is 88885 divisible by 29?
  4. 4.Is 33400 divisible by 5?
  5. 5.Is 45987 divisible by 17?
  6. 6.Is 107008 divisible by 19?
  7. 7.Is 12437 divisible by 15?
  8. 8.Is 2558 divisible by 3?
  9. 9.Is 53510 divisible by 30?
  10. 10.Is 59385 divisible by 15?
  11. 11.Is 13014 divisible by 9?
  12. 12.Is 99528 divisible by 20?
  13. 13.Is 66374 divisible by 11?
  14. 14.Is 9282 divisible by 17?
  15. 15.Is 7392 divisible by 8?
  16. 16.Is 33648 divisible by 5?
  17. 17.Is 71158 divisible by 12?
  18. 18.Is 112464 divisible by 24?
  19. 19.Is 9043 divisible by 9?
  20. 20.Is 24000 divisible by 8?
  21. 21.Is 96192 divisible by 24?
  22. 22.Is 4597 divisible by 20?
  23. 23.Is 3020 divisible by 3?
  24. 24.Is 6292 divisible by 11?
  25. 25.Is 2955 divisible by 3?
  26. 26.Is 26040 divisible by 10?
  27. 27.Is 3736 divisible by 3?
  28. 28.Is 22094 divisible by 7?
  29. 29.Is 112255 divisible by 17?
  30. 30.Is 1084 divisible by 13?
  31. 31.Is 15444 divisible by 9?
  32. 32.Is 28684 divisible by 7?
  33. 33.Is 30753 divisible by 19?
  34. 34.Is 5451 divisible by 6?
  35. 35.Is 25519 divisible by 29?
  36. 36.Is 39845 divisible by 8?
  37. 37.Is 120866 divisible by 18?
  38. 38.Is 17060 divisible by 20?
  39. 39.Is 77914 divisible by 17?
  40. 40.Is 63156 divisible by 12?

Answer key

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

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