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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 788 · 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 8291 divisible by 9?
  2. 2.Is 12653 divisible by 2?
  3. 3.Is 109249 divisible by 20?
  4. 4.Is 84796 divisible by 17?
  5. 5.Is 55962 divisible by 11?
  6. 6.Is 83247 divisible by 12?
  7. 7.Is 21360 divisible by 8?
  8. 8.Is 59784 divisible by 24?
  9. 9.Is 114798 divisible by 19?
  10. 10.Is 69408 divisible by 29?
  11. 11.Is 6551 divisible by 2?
  12. 12.Is 7159 divisible by 6?
  13. 13.Is 3652 divisible by 11?
  14. 14.Is 101038 divisible by 17?
  15. 15.Is 43096 divisible by 7?
  16. 16.Is 49878 divisible by 17?
  17. 17.Is 194155 divisible by 29?
  18. 18.Is 26824 divisible by 4?
  19. 19.Is 22310 divisible by 5?
  20. 20.Is 12356 divisible by 30?
  21. 21.Is 19154 divisible by 6?
  22. 22.Is 39491 divisible by 23?
  23. 23.Is 57120 divisible by 17?
  24. 24.Is 46837 divisible by 7?
  25. 25.Is 9887 divisible by 11?
  26. 26.Is 11330 divisible by 2?
  27. 27.Is 101520 divisible by 15?
  28. 28.Is 349 divisible by 5?
  29. 29.Is 91788 divisible by 23?
  30. 30.Is 13795 divisible by 8?
  31. 31.Is 181511 divisible by 29?
  32. 32.Is 8132 divisible by 2?
  33. 33.Is 54619 divisible by 15?
  34. 34.Is 32918 divisible by 9?
  35. 35.Is 89439 divisible by 13?
  36. 36.Is 14581 divisible by 7?
  37. 37.Is 32790 divisible by 5?
  38. 38.Is 1487 divisible by 12?
  39. 39.Is 15544 divisible by 9?
  40. 40.Is 89670 divisible by 30?

Answer key

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

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