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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 930 · 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 5197 divisible by 2?
  2. 2.Is 30682 divisible by 6?
  3. 3.Is 10562 divisible by 23?
  4. 4.Is 34253 divisible by 9?
  5. 5.Is 45912 divisible by 12?
  6. 6.Is 48529 divisible by 7?
  7. 7.Is 28875 divisible by 7?
  8. 8.Is 77454 divisible by 18?
  9. 9.Is 28398 divisible by 29?
  10. 10.Is 10391 divisible by 2?
  11. 11.Is 19446 divisible by 19?
  12. 12.Is 2868 divisible by 3?
  13. 13.Is 17691 divisible by 3?
  14. 14.Is 8690 divisible by 5?
  15. 15.Is 74492 divisible by 11?
  16. 16.Is 3516 divisible by 12?
  17. 17.Is 2641 divisible by 7?
  18. 18.Is 32446 divisible by 12?
  19. 19.Is 10065 divisible by 4?
  20. 20.Is 14886 divisible by 3?
  21. 21.Is 85 divisible by 2?
  22. 22.Is 36234 divisible by 8?
  23. 23.Is 10495 divisible by 3?
  24. 24.Is 39314 divisible by 6?
  25. 25.Is 21318 divisible by 15?
  26. 26.Is 123104 divisible by 20?
  27. 27.Is 26378 divisible by 4?
  28. 28.Is 81718 divisible by 13?
  29. 29.Is 43819 divisible by 29?
  30. 30.Is 17595 divisible by 9?
  31. 31.Is 87704 divisible by 19?
  32. 32.Is 55286 divisible by 20?
  33. 33.Is 754 divisible by 4?
  34. 34.Is 33690 divisible by 15?
  35. 35.Is 14340 divisible by 15?
  36. 36.Is 15317 divisible by 4?
  37. 37.Is 37512 divisible by 24?
  38. 38.Is 67640 divisible by 19?
  39. 39.Is 24565 divisible by 5?
  40. 40.Is 323 divisible by 2?

Answer key

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

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