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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 313 · 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 4380 divisible by 12?
  2. 2.Is 17499 divisible by 4?
  3. 3.Is 107677 divisible by 29?
  4. 4.Is 139200 divisible by 24?
  5. 5.Is 49742 divisible by 15?
  6. 6.Is 100374 divisible by 20?
  7. 7.Is 17973 divisible by 4?
  8. 8.Is 6394 divisible by 2?
  9. 9.Is 22241 divisible by 4?
  10. 10.Is 26344 divisible by 4?
  11. 11.Is 60825 divisible by 15?
  12. 12.Is 2239 divisible by 3?
  13. 13.Is 63255 divisible by 17?
  14. 14.Is 33277 divisible by 10?
  15. 15.Is 54049 divisible by 17?
  16. 16.Is 8530 divisible by 7?
  17. 17.Is 41145 divisible by 6?
  18. 18.Is 27876 divisible by 23?
  19. 19.Is 3514 divisible by 3?
  20. 20.Is 156446 divisible by 23?
  21. 21.Is 15507 divisible by 3?
  22. 22.Is 637 divisible by 7?
  23. 23.Is 30498 divisible by 11?
  24. 24.Is 3919 divisible by 3?
  25. 25.Is 30162 divisible by 20?
  26. 26.Is 48887 divisible by 19?
  27. 27.Is 13652 divisible by 3?
  28. 28.Is 4032 divisible by 30?
  29. 29.Is 39318 divisible by 6?
  30. 30.Is 34255 divisible by 12?
  31. 31.Is 7207 divisible by 9?
  32. 32.Is 26514 divisible by 4?
  33. 33.Is 119038 divisible by 24?
  34. 34.Is 9767 divisible by 12?
  35. 35.Is 15462 divisible by 6?
  36. 36.Is 13518 divisible by 9?
  37. 37.Is 10015 divisible by 3?
  38. 38.Is 14906 divisible by 5?
  39. 39.Is 4794 divisible by 15?
  40. 40.Is 11105 divisible by 15?

Answer key

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

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