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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 593 · 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 12352 divisible by 2?
  2. 2.Is 76723 divisible by 12?
  3. 3.Is 50515 divisible by 12?
  4. 4.Is 3879 divisible by 3?
  5. 5.Is 10360 divisible by 8?
  6. 6.Is 9005 divisible by 2?
  7. 7.Is 86148 divisible by 15?
  8. 8.Is 183930 divisible by 30?
  9. 9.Is 117507 divisible by 23?
  10. 10.Is 53952 divisible by 30?
  11. 11.Is 74398 divisible by 29?
  12. 12.Is 3835 divisible by 2?
  13. 13.Is 23447 divisible by 20?
  14. 14.Is 62919 divisible by 12?
  15. 15.Is 22980 divisible by 20?
  16. 16.Is 66300 divisible by 17?
  17. 17.Is 44643 divisible by 10?
  18. 18.Is 16016 divisible by 8?
  19. 19.Is 19008 divisible by 8?
  20. 20.Is 159283 divisible by 23?
  21. 21.Is 17419 divisible by 3?
  22. 22.Is 8619 divisible by 8?
  23. 23.Is 88752 divisible by 24?
  24. 24.Is 66643 divisible by 11?
  25. 25.Is 42214 divisible by 11?
  26. 26.Is 141694 divisible by 29?
  27. 27.Is 32131 divisible by 23?
  28. 28.Is 28089 divisible by 9?
  29. 29.Is 178530 divisible by 30?
  30. 30.Is 9425 divisible by 3?
  31. 31.Is 6726 divisible by 2?
  32. 32.Is 31833 divisible by 10?
  33. 33.Is 17829 divisible by 4?
  34. 34.Is 65569 divisible by 23?
  35. 35.Is 110923 divisible by 18?
  36. 36.Is 72410 divisible by 13?
  37. 37.Is 13493 divisible by 3?
  38. 38.Is 33481 divisible by 7?
  39. 39.Is 26160 divisible by 15?
  40. 40.Is 38683 divisible by 10?

Answer key

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

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