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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 897 · 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 9690 divisible by 3?
  2. 2.Is 14106 divisible by 4?
  3. 3.Is 10440 divisible by 20?
  4. 4.Is 14976 divisible by 12?
  5. 5.Is 14383 divisible by 17?
  6. 6.Is 5026 divisible by 7?
  7. 7.Is 45387 divisible by 8?
  8. 8.Is 64216 divisible by 23?
  9. 9.Is 18560 divisible by 20?
  10. 10.Is 66521 divisible by 17?
  11. 11.Is 54196 divisible by 17?
  12. 12.Is 15309 divisible by 9?
  13. 13.Is 27336 divisible by 17?
  14. 14.Is 23056 divisible by 15?
  15. 15.Is 12736 divisible by 8?
  16. 16.Is 987 divisible by 3?
  17. 17.Is 24804 divisible by 6?
  18. 18.Is 9444 divisible by 4?
  19. 19.Is 55880 divisible by 19?
  20. 20.Is 15144 divisible by 12?
  21. 21.Is 91276 divisible by 19?
  22. 22.Is 22943 divisible by 6?
  23. 23.Is 32618 divisible by 8?
  24. 24.Is 42053 divisible by 24?
  25. 25.Is 71298 divisible by 17?
  26. 26.Is 71688 divisible by 29?
  27. 27.Is 737 divisible by 2?
  28. 28.Is 19610 divisible by 8?
  29. 29.Is 8103 divisible by 2?
  30. 30.Is 225 divisible by 11?
  31. 31.Is 24280 divisible by 20?
  32. 32.Is 37743 divisible by 7?
  33. 33.Is 91698 divisible by 17?
  34. 34.Is 5956 divisible by 5?
  35. 35.Is 25564 divisible by 7?
  36. 36.Is 17417 divisible by 3?
  37. 37.Is 18520 divisible by 6?
  38. 38.Is 11046 divisible by 30?
  39. 39.Is 39405 divisible by 7?
  40. 40.Is 24570 divisible by 6?

Answer key

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

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