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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 863 · 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 125567 divisible by 29?
  2. 2.Is 65060 divisible by 20?
  3. 3.Is 14175 divisible by 11?
  4. 4.Is 83222 divisible by 13?
  5. 5.Is 45890 divisible by 10?
  6. 6.Is 58412 divisible by 11?
  7. 7.Is 4386 divisible by 20?
  8. 8.Is 89256 divisible by 19?
  9. 9.Is 5254 divisible by 2?
  10. 10.Is 7925 divisible by 3?
  11. 11.Is 14830 divisible by 5?
  12. 12.Is 949 divisible by 2?
  13. 13.Is 4927 divisible by 12?
  14. 14.Is 17120 divisible by 20?
  15. 15.Is 11899 divisible by 18?
  16. 16.Is 6006 divisible by 5?
  17. 17.Is 2356 divisible by 2?
  18. 18.Is 7281 divisible by 3?
  19. 19.Is 78187 divisible by 18?
  20. 20.Is 84829 divisible by 15?
  21. 21.Is 93413 divisible by 20?
  22. 22.Is 61767 divisible by 9?
  23. 23.Is 91440 divisible by 15?
  24. 24.Is 3071 divisible by 4?
  25. 25.Is 24687 divisible by 9?
  26. 26.Is 10765 divisible by 4?
  27. 27.Is 21532 divisible by 7?
  28. 28.Is 5017 divisible by 4?
  29. 29.Is 9339 divisible by 2?
  30. 30.Is 57609 divisible by 9?
  31. 31.Is 31033 divisible by 6?
  32. 32.Is 12563 divisible by 2?
  33. 33.Is 160710 divisible by 30?
  34. 34.Is 129071 divisible by 19?
  35. 35.Is 58752 divisible by 18?
  36. 36.Is 9591 divisible by 2?
  37. 37.Is 96684 divisible by 20?
  38. 38.Is 15300 divisible by 17?
  39. 39.Is 50593 divisible by 12?
  40. 40.Is 45695 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. yes
  12. no
  13. no
  14. yes
  15. no
  16. no
  17. yes
  18. yes
  19. no
  20. no
  21. no
  22. yes
  23. yes
  24. no
  25. yes
  26. no
  27. yes
  28. no
  29. no
  30. yes
  31. no
  32. no
  33. yes
  34. no
  35. yes
  36. no
  37. no
  38. yes
  39. no
  40. no

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