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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 939 · 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 34349 divisible by 5?
  2. 2.Is 38065 divisible by 23?
  3. 3.Is 3816 divisible by 3?
  4. 4.Is 54 divisible by 3?
  5. 5.Is 39522 divisible by 6?
  6. 6.Is 17682 divisible by 7?
  7. 7.Is 4950 divisible by 18?
  8. 8.Is 7205 divisible by 11?
  9. 9.Is 98540 divisible by 20?
  10. 10.Is 23736 divisible by 24?
  11. 11.Is 61126 divisible by 13?
  12. 12.Is 76807 divisible by 11?
  13. 13.Is 6330 divisible by 6?
  14. 14.Is 54180 divisible by 30?
  15. 15.Is 8098 divisible by 2?
  16. 16.Is 5904 divisible by 23?
  17. 17.Is 111113 divisible by 17?
  18. 18.Is 35511 divisible by 11?
  19. 19.Is 59048 divisible by 10?
  20. 20.Is 29240 divisible by 10?
  21. 21.Is 192930 divisible by 30?
  22. 22.Is 12440 divisible by 17?
  23. 23.Is 16866 divisible by 7?
  24. 24.Is 61320 divisible by 20?
  25. 25.Is 36123 divisible by 15?
  26. 26.Is 46321 divisible by 23?
  27. 27.Is 40475 divisible by 8?
  28. 28.Is 13846 divisible by 3?
  29. 29.Is 181685 divisible by 29?
  30. 30.Is 62158 divisible by 29?
  31. 31.Is 49166 divisible by 12?
  32. 32.Is 18213 divisible by 23?
  33. 33.Is 123337 divisible by 29?
  34. 34.Is 24519 divisible by 23?
  35. 35.Is 20790 divisible by 10?
  36. 36.Is 46134 divisible by 9?
  37. 37.Is 73000 divisible by 18?
  38. 38.Is 96860 divisible by 20?
  39. 39.Is 6692 divisible by 3?
  40. 40.Is 204429 divisible by 30?

Answer key

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

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