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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 866 · 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 11742 divisible by 3?
  2. 2.Is 7279 divisible by 29?
  3. 3.Is 131081 divisible by 29?
  4. 4.Is 28824 divisible by 6?
  5. 5.Is 24265 divisible by 23?
  6. 6.Is 25764 divisible by 19?
  7. 7.Is 18169 divisible by 8?
  8. 8.Is 77311 divisible by 13?
  9. 9.Is 34560 divisible by 18?
  10. 10.Is 49030 divisible by 9?
  11. 11.Is 67684 divisible by 12?
  12. 12.Is 90375 divisible by 15?
  13. 13.Is 1008 divisible by 2?
  14. 14.Is 75939 divisible by 20?
  15. 15.Is 11684 divisible by 30?
  16. 16.Is 22080 divisible by 5?
  17. 17.Is 15249 divisible by 13?
  18. 18.Is 6822 divisible by 9?
  19. 19.Is 8055 divisible by 9?
  20. 20.Is 13191 divisible by 3?
  21. 21.Is 18520 divisible by 5?
  22. 22.Is 96165 divisible by 15?
  23. 23.Is 115137 divisible by 17?
  24. 24.Is 113093 divisible by 18?
  25. 25.Is 193643 divisible by 29?
  26. 26.Is 16779 divisible by 9?
  27. 27.Is 33345 divisible by 5?
  28. 28.Is 25495 divisible by 4?
  29. 29.Is 72284 divisible by 17?
  30. 30.Is 16160 divisible by 5?
  31. 31.Is 20543 divisible by 6?
  32. 32.Is 48985 divisible by 13?
  33. 33.Is 51840 divisible by 24?
  34. 34.Is 21803 divisible by 6?
  35. 35.Is 76574 divisible by 29?
  36. 36.Is 22422 divisible by 9?
  37. 37.Is 21184 divisible by 20?
  38. 38.Is 111203 divisible by 23?
  39. 39.Is 1872 divisible by 6?
  40. 40.Is 121007 divisible by 18?

Answer key

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

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