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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 357 · 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 24357 divisible by 11?
  2. 2.Is 23698 divisible by 8?
  3. 3.Is 15923 divisible by 5?
  4. 4.Is 10333 divisible by 8?
  5. 5.Is 645 divisible by 15?
  6. 6.Is 6068 divisible by 3?
  7. 7.Is 200825 divisible by 29?
  8. 8.Is 14301 divisible by 4?
  9. 9.Is 31765 divisible by 20?
  10. 10.Is 124783 divisible by 19?
  11. 11.Is 164470 divisible by 29?
  12. 12.Is 10404 divisible by 18?
  13. 13.Is 20872 divisible by 10?
  14. 14.Is 50882 divisible by 29?
  15. 15.Is 35573 divisible by 24?
  16. 16.Is 85064 divisible by 15?
  17. 17.Is 28600 divisible by 10?
  18. 18.Is 10752 divisible by 3?
  19. 19.Is 4442 divisible by 2?
  20. 20.Is 94689 divisible by 29?
  21. 21.Is 33721 divisible by 19?
  22. 22.Is 5104 divisible by 5?
  23. 23.Is 11346 divisible by 2?
  24. 24.Is 8657 divisible by 2?
  25. 25.Is 23800 divisible by 6?
  26. 26.Is 51371 divisible by 29?
  27. 27.Is 27598 divisible by 4?
  28. 28.Is 52666 divisible by 17?
  29. 29.Is 15294 divisible by 9?
  30. 30.Is 81657 divisible by 13?
  31. 31.Is 1089 divisible by 11?
  32. 32.Is 14277 divisible by 4?
  33. 33.Is 1777 divisible by 12?
  34. 34.Is 15912 divisible by 24?
  35. 35.Is 4780 divisible by 2?
  36. 36.Is 96720 divisible by 24?
  37. 37.Is 34255 divisible by 23?
  38. 38.Is 127546 divisible by 29?
  39. 39.Is 18580 divisible by 6?
  40. 40.Is 34613 divisible by 19?

Answer key

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

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