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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 789 · 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 30111 divisible by 6?
  2. 2.Is 50633 divisible by 11?
  3. 3.Is 11343 divisible by 10?
  4. 4.Is 64602 divisible by 18?
  5. 5.Is 94438 divisible by 23?
  6. 6.Is 71698 divisible by 18?
  7. 7.Is 82236 divisible by 24?
  8. 8.Is 103115 divisible by 19?
  9. 9.Is 38430 divisible by 19?
  10. 10.Is 6498 divisible by 17?
  11. 11.Is 5692 divisible by 10?
  12. 12.Is 6590 divisible by 2?
  13. 13.Is 70833 divisible by 18?
  14. 14.Is 14791 divisible by 7?
  15. 15.Is 107735 divisible by 24?
  16. 16.Is 51048 divisible by 8?
  17. 17.Is 39834 divisible by 12?
  18. 18.Is 158337 divisible by 30?
  19. 19.Is 81213 divisible by 29?
  20. 20.Is 15078 divisible by 9?
  21. 21.Is 41863 divisible by 6?
  22. 22.Is 919 divisible by 3?
  23. 23.Is 5906 divisible by 13?
  24. 24.Is 28184 divisible by 24?
  25. 25.Is 11037 divisible by 2?
  26. 26.Is 59408 divisible by 17?
  27. 27.Is 40603 divisible by 11?
  28. 28.Is 36215 divisible by 19?
  29. 29.Is 31320 divisible by 5?
  30. 30.Is 21828 divisible by 6?
  31. 31.Is 4719 divisible by 2?
  32. 32.Is 11579 divisible by 8?
  33. 33.Is 40832 divisible by 8?
  34. 34.Is 20595 divisible by 15?
  35. 35.Is 31410 divisible by 15?
  36. 36.Is 32659 divisible by 5?
  37. 37.Is 173420 divisible by 29?
  38. 38.Is 15640 divisible by 5?
  39. 39.Is 137866 divisible by 29?
  40. 40.Is 67732 divisible by 17?

Answer key

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

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