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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 697 · 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 93853 divisible by 19?
  2. 2.Is 56543 divisible by 15?
  3. 3.Is 34729 divisible by 9?
  4. 4.Is 18801 divisible by 6?
  5. 5.Is 56825 divisible by 12?
  6. 6.Is 116440 divisible by 24?
  7. 7.Is 5137 divisible by 3?
  8. 8.Is 21930 divisible by 15?
  9. 9.Is 15212 divisible by 3?
  10. 10.Is 36572 divisible by 9?
  11. 11.Is 47618 divisible by 24?
  12. 12.Is 4754 divisible by 2?
  13. 13.Is 50497 divisible by 8?
  14. 14.Is 68486 divisible by 10?
  15. 15.Is 80524 divisible by 19?
  16. 16.Is 162579 divisible by 30?
  17. 17.Is 40860 divisible by 6?
  18. 18.Is 54711 divisible by 8?
  19. 19.Is 4374 divisible by 18?
  20. 20.Is 17511 divisible by 18?
  21. 21.Is 60022 divisible by 24?
  22. 22.Is 47920 divisible by 30?
  23. 23.Is 34944 divisible by 12?
  24. 24.Is 470 divisible by 3?
  25. 25.Is 14864 divisible by 3?
  26. 26.Is 28566 divisible by 6?
  27. 27.Is 110100 divisible by 20?
  28. 28.Is 60853 divisible by 18?
  29. 29.Is 37161 divisible by 6?
  30. 30.Is 102850 divisible by 29?
  31. 31.Is 17162 divisible by 24?
  32. 32.Is 4095 divisible by 13?
  33. 33.Is 24058 divisible by 23?
  34. 34.Is 93759 divisible by 20?
  35. 35.Is 9217 divisible by 4?
  36. 36.Is 33390 divisible by 11?
  37. 37.Is 23432 divisible by 29?
  38. 38.Is 78709 divisible by 30?
  39. 39.Is 79924 divisible by 15?
  40. 40.Is 5984 divisible by 2?

Answer key

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

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