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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 737 · 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 90275 divisible by 29?
  2. 2.Is 119418 divisible by 19?
  3. 3.Is 12349 divisible by 9?
  4. 4.Is 53380 divisible by 17?
  5. 5.Is 119976 divisible by 18?
  6. 6.Is 129564 divisible by 23?
  7. 7.Is 3577 divisible by 6?
  8. 8.Is 19626 divisible by 3?
  9. 9.Is 5704 divisible by 2?
  10. 10.Is 108681 divisible by 17?
  11. 11.Is 2785 divisible by 5?
  12. 12.Is 90100 divisible by 17?
  13. 13.Is 44584 divisible by 24?
  14. 14.Is 10474 divisible by 4?
  15. 15.Is 1295 divisible by 7?
  16. 16.Is 39943 divisible by 10?
  17. 17.Is 35945 divisible by 6?
  18. 18.Is 39351 divisible by 12?
  19. 19.Is 12852 divisible by 12?
  20. 20.Is 29097 divisible by 5?
  21. 21.Is 52751 divisible by 15?
  22. 22.Is 42864 divisible by 12?
  23. 23.Is 109054 divisible by 23?
  24. 24.Is 22412 divisible by 4?
  25. 25.Is 26246 divisible by 11?
  26. 26.Is 110584 divisible by 20?
  27. 27.Is 76406 divisible by 23?
  28. 28.Is 15119 divisible by 13?
  29. 29.Is 20816 divisible by 24?
  30. 30.Is 93132 divisible by 18?
  31. 31.Is 17342 divisible by 9?
  32. 32.Is 14913 divisible by 9?
  33. 33.Is 4962 divisible by 3?
  34. 34.Is 117503 divisible by 19?
  35. 35.Is 12472 divisible by 4?
  36. 36.Is 13395 divisible by 2?
  37. 37.Is 10641 divisible by 4?
  38. 38.Is 3937 divisible by 5?
  39. 39.Is 3888 divisible by 9?
  40. 40.Is 76646 divisible by 20?

Answer key

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

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