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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 475 · 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 44912 divisible by 8?
  2. 2.Is 21336 divisible by 7?
  3. 3.Is 97901 divisible by 19?
  4. 4.Is 49623 divisible by 11?
  5. 5.Is 55519 divisible by 8?
  6. 6.Is 18566 divisible by 15?
  7. 7.Is 61919 divisible by 20?
  8. 8.Is 68127 divisible by 11?
  9. 9.Is 48664 divisible by 11?
  10. 10.Is 47032 divisible by 7?
  11. 11.Is 38233 divisible by 17?
  12. 12.Is 151728 divisible by 24?
  13. 13.Is 53825 divisible by 10?
  14. 14.Is 64490 divisible by 10?
  15. 15.Is 39977 divisible by 23?
  16. 16.Is 60693 divisible by 15?
  17. 17.Is 11824 divisible by 4?
  18. 18.Is 1603 divisible by 7?
  19. 19.Is 57596 divisible by 17?
  20. 20.Is 8466 divisible by 10?
  21. 21.Is 67812 divisible by 17?
  22. 22.Is 12673 divisible by 29?
  23. 23.Is 105408 divisible by 18?
  24. 24.Is 42506 divisible by 12?
  25. 25.Is 42442 divisible by 8?
  26. 26.Is 3457 divisible by 2?
  27. 27.Is 17295 divisible by 15?
  28. 28.Is 84790 divisible by 18?
  29. 29.Is 12704 divisible by 4?
  30. 30.Is 18126 divisible by 9?
  31. 31.Is 151442 divisible by 30?
  32. 32.Is 10803 divisible by 13?
  33. 33.Is 51489 divisible by 8?
  34. 34.Is 12762 divisible by 18?
  35. 35.Is 55055 divisible by 15?
  36. 36.Is 4886 divisible by 8?
  37. 37.Is 425 divisible by 3?
  38. 38.Is 14654 divisible by 17?
  39. 39.Is 27518 divisible by 8?
  40. 40.Is 3397 divisible by 4?

Answer key

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

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