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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 41 · 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 28342 divisible by 11?
  2. 2.Is 23272 divisible by 10?
  3. 3.Is 2558 divisible by 7?
  4. 4.Is 120000 divisible by 30?
  5. 5.Is 12572 divisible by 23?
  6. 6.Is 7297 divisible by 6?
  7. 7.Is 24580 divisible by 10?
  8. 8.Is 56026 divisible by 9?
  9. 9.Is 55422 divisible by 9?
  10. 10.Is 5062 divisible by 2?
  11. 11.Is 34410 divisible by 10?
  12. 12.Is 57300 divisible by 30?
  13. 13.Is 36936 divisible by 24?
  14. 14.Is 5589 divisible by 3?
  15. 15.Is 108789 divisible by 19?
  16. 16.Is 24242 divisible by 23?
  17. 17.Is 15865 divisible by 4?
  18. 18.Is 14995 divisible by 11?
  19. 19.Is 42456 divisible by 12?
  20. 20.Is 13436 divisible by 3?
  21. 21.Is 16470 divisible by 5?
  22. 22.Is 4327 divisible by 2?
  23. 23.Is 30975 divisible by 8?
  24. 24.Is 46020 divisible by 13?
  25. 25.Is 50336 divisible by 11?
  26. 26.Is 140408 divisible by 29?
  27. 27.Is 8964 divisible by 2?
  28. 28.Is 9972 divisible by 6?
  29. 29.Is 18649 divisible by 4?
  30. 30.Is 63880 divisible by 20?
  31. 31.Is 42550 divisible by 30?
  32. 32.Is 4818 divisible by 11?
  33. 33.Is 135746 divisible by 23?
  34. 34.Is 11556 divisible by 6?
  35. 35.Is 118659 divisible by 17?
  36. 36.Is 39135 divisible by 7?
  37. 37.Is 41217 divisible by 11?
  38. 38.Is 33009 divisible by 8?
  39. 39.Is 23291 divisible by 19?
  40. 40.Is 41824 divisible by 8?

Answer key

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

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