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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 217 · 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 9648 divisible by 18?
  2. 2.Is 6028 divisible by 9?
  3. 3.Is 3500 divisible by 4?
  4. 4.Is 108605 divisible by 18?
  5. 5.Is 15500 divisible by 3?
  6. 6.Is 176479 divisible by 29?
  7. 7.Is 13607 divisible by 3?
  8. 8.Is 124790 divisible by 30?
  9. 9.Is 18623 divisible by 13?
  10. 10.Is 2925 divisible by 13?
  11. 11.Is 82295 divisible by 24?
  12. 12.Is 46348 divisible by 24?
  13. 13.Is 25517 divisible by 17?
  14. 14.Is 8632 divisible by 13?
  15. 15.Is 20600 divisible by 6?
  16. 16.Is 83914 divisible by 15?
  17. 17.Is 13538 divisible by 4?
  18. 18.Is 18765 divisible by 18?
  19. 19.Is 12708 divisible by 4?
  20. 20.Is 40015 divisible by 29?
  21. 21.Is 167612 divisible by 29?
  22. 22.Is 143382 divisible by 23?
  23. 23.Is 26239 divisible by 4?
  24. 24.Is 41346 divisible by 9?
  25. 25.Is 20316 divisible by 12?
  26. 26.Is 34788 divisible by 7?
  27. 27.Is 14883 divisible by 8?
  28. 28.Is 105938 divisible by 23?
  29. 29.Is 148750 divisible by 24?
  30. 30.Is 5835 divisible by 2?
  31. 31.Is 96059 divisible by 29?
  32. 32.Is 21567 divisible by 17?
  33. 33.Is 2515 divisible by 2?
  34. 34.Is 4794 divisible by 6?
  35. 35.Is 27675 divisible by 5?
  36. 36.Is 38996 divisible by 29?
  37. 37.Is 95988 divisible by 19?
  38. 38.Is 9329 divisible by 20?
  39. 39.Is 24900 divisible by 10?
  40. 40.Is 37191 divisible by 11?

Answer key

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

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