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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 320 · 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 78315 divisible by 23?
  2. 2.Is 11061 divisible by 10?
  3. 3.Is 77956 divisible by 24?
  4. 4.Is 96 divisible by 2?
  5. 5.Is 31599 divisible by 9?
  6. 6.Is 17976 divisible by 6?
  7. 7.Is 18733 divisible by 13?
  8. 8.Is 50416 divisible by 8?
  9. 9.Is 89280 divisible by 20?
  10. 10.Is 49813 divisible by 8?
  11. 11.Is 38484 divisible by 12?
  12. 12.Is 34892 divisible by 13?
  13. 13.Is 25509 divisible by 11?
  14. 14.Is 11349 divisible by 4?
  15. 15.Is 15045 divisible by 3?
  16. 16.Is 2132 divisible by 2?
  17. 17.Is 67943 divisible by 30?
  18. 18.Is 26012 divisible by 7?
  19. 19.Is 27817 divisible by 5?
  20. 20.Is 113832 divisible by 17?
  21. 21.Is 103651 divisible by 30?
  22. 22.Is 48961 divisible by 9?
  23. 23.Is 83027 divisible by 29?
  24. 24.Is 88989 divisible by 24?
  25. 25.Is 109003 divisible by 19?
  26. 26.Is 15340 divisible by 13?
  27. 27.Is 13912 divisible by 2?
  28. 28.Is 24609 divisible by 7?
  29. 29.Is 13648 divisible by 8?
  30. 30.Is 37468 divisible by 17?
  31. 31.Is 77129 divisible by 17?
  32. 32.Is 1344 divisible by 7?
  33. 33.Is 34371 divisible by 10?
  34. 34.Is 21832 divisible by 9?
  35. 35.Is 10071 divisible by 9?
  36. 36.Is 28849 divisible by 17?
  37. 37.Is 13709 divisible by 15?
  38. 38.Is 1474 divisible by 12?
  39. 39.Is 39576 divisible by 6?
  40. 40.Is 28027 divisible by 23?

Answer key

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

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