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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 123 · 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 9318 divisible by 19?
  2. 2.Is 36575 divisible by 19?
  3. 3.Is 3345 divisible by 15?
  4. 4.Is 18411 divisible by 3?
  5. 5.Is 51984 divisible by 24?
  6. 6.Is 70840 divisible by 20?
  7. 7.Is 191293 divisible by 29?
  8. 8.Is 30404 divisible by 5?
  9. 9.Is 31525 divisible by 17?
  10. 10.Is 110491 divisible by 29?
  11. 11.Is 79737 divisible by 20?
  12. 12.Is 31005 divisible by 5?
  13. 13.Is 11936 divisible by 12?
  14. 14.Is 67362 divisible by 20?
  15. 15.Is 24196 divisible by 23?
  16. 16.Is 79019 divisible by 18?
  17. 17.Is 33669 divisible by 7?
  18. 18.Is 22122 divisible by 9?
  19. 19.Is 22036 divisible by 24?
  20. 20.Is 3320 divisible by 29?
  21. 21.Is 34641 divisible by 11?
  22. 22.Is 61785 divisible by 15?
  23. 23.Is 4134 divisible by 2?
  24. 24.Is 5676 divisible by 4?
  25. 25.Is 30642 divisible by 20?
  26. 26.Is 56345 divisible by 19?
  27. 27.Is 33349 divisible by 7?
  28. 28.Is 24157 divisible by 17?
  29. 29.Is 62494 divisible by 15?
  30. 30.Is 11320 divisible by 4?
  31. 31.Is 64786 divisible by 30?
  32. 32.Is 21275 divisible by 15?
  33. 33.Is 119981 divisible by 24?
  34. 34.Is 23073 divisible by 6?
  35. 35.Is 19073 divisible by 3?
  36. 36.Is 11650 divisible by 2?
  37. 37.Is 78122 divisible by 17?
  38. 38.Is 32844 divisible by 7?
  39. 39.Is 3834 divisible by 2?
  40. 40.Is 22104 divisible by 7?

Answer key

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

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