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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 600 · 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 10797 divisible by 6?
  2. 2.Is 34618 divisible by 19?
  3. 3.Is 40696 divisible by 7?
  4. 4.Is 69352 divisible by 24?
  5. 5.Is 24955 divisible by 5?
  6. 6.Is 8405 divisible by 2?
  7. 7.Is 24871 divisible by 5?
  8. 8.Is 11978 divisible by 13?
  9. 9.Is 18348 divisible by 4?
  10. 10.Is 106166 divisible by 17?
  11. 11.Is 62745 divisible by 9?
  12. 12.Is 1835 divisible by 7?
  13. 13.Is 10815 divisible by 15?
  14. 14.Is 83252 divisible by 13?
  15. 15.Is 4529 divisible by 7?
  16. 16.Is 2056 divisible by 2?
  17. 17.Is 67272 divisible by 12?
  18. 18.Is 89851 divisible by 13?
  19. 19.Is 60102 divisible by 18?
  20. 20.Is 123798 divisible by 29?
  21. 21.Is 1625 divisible by 13?
  22. 22.Is 137454 divisible by 23?
  23. 23.Is 1499 divisible by 4?
  24. 24.Is 12155 divisible by 4?
  25. 25.Is 22881 divisible by 4?
  26. 26.Is 96577 divisible by 15?
  27. 27.Is 17940 divisible by 6?
  28. 28.Is 77517 divisible by 29?
  29. 29.Is 39857 divisible by 7?
  30. 30.Is 14664 divisible by 8?
  31. 31.Is 183788 divisible by 29?
  32. 32.Is 35873 divisible by 29?
  33. 33.Is 53083 divisible by 13?
  34. 34.Is 16058 divisible by 7?
  35. 35.Is 13323 divisible by 17?
  36. 36.Is 35378 divisible by 7?
  37. 37.Is 2015 divisible by 18?
  38. 38.Is 24468 divisible by 6?
  39. 39.Is 747 divisible by 2?
  40. 40.Is 25550 divisible by 7?

Answer key

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

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