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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 115 · 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 91574 divisible by 23?
  2. 2.Is 66727 divisible by 15?
  3. 3.Is 7975 divisible by 2?
  4. 4.Is 13251 divisible by 6?
  5. 5.Is 53804 divisible by 18?
  6. 6.Is 60984 divisible by 18?
  7. 7.Is 8706 divisible by 3?
  8. 8.Is 40976 divisible by 13?
  9. 9.Is 136983 divisible by 23?
  10. 10.Is 37814 divisible by 7?
  11. 11.Is 53739 divisible by 9?
  12. 12.Is 15423 divisible by 7?
  13. 13.Is 44272 divisible by 7?
  14. 14.Is 13684 divisible by 15?
  15. 15.Is 12263 divisible by 5?
  16. 16.Is 12725 divisible by 4?
  17. 17.Is 27858 divisible by 6?
  18. 18.Is 11420 divisible by 15?
  19. 19.Is 42108 divisible by 20?
  20. 20.Is 872 divisible by 4?
  21. 21.Is 58435 divisible by 13?
  22. 22.Is 33464 divisible by 18?
  23. 23.Is 42720 divisible by 24?
  24. 24.Is 14882 divisible by 4?
  25. 25.Is 118275 divisible by 19?
  26. 26.Is 39712 divisible by 8?
  27. 27.Is 40914 divisible by 6?
  28. 28.Is 13114 divisible by 17?
  29. 29.Is 29042 divisible by 7?
  30. 30.Is 12995 divisible by 2?
  31. 31.Is 113696 divisible by 23?
  32. 32.Is 25500 divisible by 12?
  33. 33.Is 19105 divisible by 5?
  34. 34.Is 113470 divisible by 29?
  35. 35.Is 1416 divisible by 2?
  36. 36.Is 39193 divisible by 12?
  37. 37.Is 28878 divisible by 6?
  38. 38.Is 6489 divisible by 7?
  39. 39.Is 85318 divisible by 13?
  40. 40.Is 2679 divisible by 3?

Answer key

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

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