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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 460 · 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 21618 divisible by 9?
  2. 2.Is 6600 divisible by 20?
  3. 3.Is 20263 divisible by 23?
  4. 4.Is 94367 divisible by 17?
  5. 5.Is 54440 divisible by 8?
  6. 6.Is 6007 divisible by 4?
  7. 7.Is 66442 divisible by 10?
  8. 8.Is 3905 divisible by 4?
  9. 9.Is 71084 divisible by 17?
  10. 10.Is 7542 divisible by 6?
  11. 11.Is 21240 divisible by 18?
  12. 12.Is 28130 divisible by 7?
  13. 13.Is 88887 divisible by 20?
  14. 14.Is 150903 divisible by 23?
  15. 15.Is 34607 divisible by 5?
  16. 16.Is 32881 divisible by 7?
  17. 17.Is 10159 divisible by 2?
  18. 18.Is 14581 divisible by 29?
  19. 19.Is 16399 divisible by 17?
  20. 20.Is 6548 divisible by 3?
  21. 21.Is 10950 divisible by 10?
  22. 22.Is 18540 divisible by 20?
  23. 23.Is 21945 divisible by 19?
  24. 24.Is 122292 divisible by 18?
  25. 25.Is 68874 divisible by 13?
  26. 26.Is 37140 divisible by 15?
  27. 27.Is 102196 divisible by 17?
  28. 28.Is 26195 divisible by 10?
  29. 29.Is 188460 divisible by 30?
  30. 30.Is 14056 divisible by 6?
  31. 31.Is 145609 divisible by 29?
  32. 32.Is 24848 divisible by 24?
  33. 33.Is 78977 divisible by 24?
  34. 34.Is 59272 divisible by 11?
  35. 35.Is 1857 divisible by 4?
  36. 36.Is 152641 divisible by 24?
  37. 37.Is 12834 divisible by 6?
  38. 38.Is 2441 divisible by 5?
  39. 39.Is 23820 divisible by 4?
  40. 40.Is 20248 divisible by 3?

Answer key

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

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