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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 117 · 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 12531 divisible by 3?
  2. 2.Is 60499 divisible by 9?
  3. 3.Is 71900 divisible by 20?
  4. 4.Is 15416 divisible by 6?
  5. 5.Is 12615 divisible by 5?
  6. 6.Is 11993 divisible by 7?
  7. 7.Is 3080 divisible by 4?
  8. 8.Is 82564 divisible by 15?
  9. 9.Is 32345 divisible by 8?
  10. 10.Is 3746 divisible by 2?
  11. 11.Is 34792 divisible by 12?
  12. 12.Is 73485 divisible by 23?
  13. 13.Is 372 divisible by 5?
  14. 14.Is 69380 divisible by 15?
  15. 15.Is 25403 divisible by 10?
  16. 16.Is 15706 divisible by 3?
  17. 17.Is 102977 divisible by 24?
  18. 18.Is 86517 divisible by 29?
  19. 19.Is 17879 divisible by 3?
  20. 20.Is 113639 divisible by 19?
  21. 21.Is 106927 divisible by 23?
  22. 22.Is 37089 divisible by 6?
  23. 23.Is 53085 divisible by 15?
  24. 24.Is 33692 divisible by 18?
  25. 25.Is 110700 divisible by 20?
  26. 26.Is 30290 divisible by 10?
  27. 27.Is 46560 divisible by 10?
  28. 28.Is 1986 divisible by 5?
  29. 29.Is 59376 divisible by 24?
  30. 30.Is 99336 divisible by 24?
  31. 31.Is 46019 divisible by 15?
  32. 32.Is 7400 divisible by 11?
  33. 33.Is 56771 divisible by 13?
  34. 34.Is 19008 divisible by 11?
  35. 35.Is 12746 divisible by 9?
  36. 36.Is 40977 divisible by 10?
  37. 37.Is 5875 divisible by 6?
  38. 38.Is 27259 divisible by 6?
  39. 39.Is 24115 divisible by 7?
  40. 40.Is 37017 divisible by 9?

Answer key

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

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