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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 838 · 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 37791 divisible by 17?
  2. 2.Is 16341 divisible by 10?
  3. 3.Is 50457 divisible by 15?
  4. 4.Is 102850 divisible by 17?
  5. 5.Is 135033 divisible by 23?
  6. 6.Is 12790 divisible by 24?
  7. 7.Is 6480 divisible by 10?
  8. 8.Is 90828 divisible by 29?
  9. 9.Is 108657 divisible by 30?
  10. 10.Is 20862 divisible by 9?
  11. 11.Is 33571 divisible by 10?
  12. 12.Is 12147 divisible by 11?
  13. 13.Is 106955 divisible by 23?
  14. 14.Is 85295 divisible by 18?
  15. 15.Is 23480 divisible by 15?
  16. 16.Is 28319 divisible by 5?
  17. 17.Is 10623 divisible by 6?
  18. 18.Is 5705 divisible by 3?
  19. 19.Is 37716 divisible by 7?
  20. 20.Is 120224 divisible by 30?
  21. 21.Is 31728 divisible by 6?
  22. 22.Is 94882 divisible by 15?
  23. 23.Is 4045 divisible by 5?
  24. 24.Is 79898 divisible by 13?
  25. 25.Is 11155 divisible by 23?
  26. 26.Is 21461 divisible by 11?
  27. 27.Is 9807 divisible by 23?
  28. 28.Is 16065 divisible by 9?
  29. 29.Is 53252 divisible by 13?
  30. 30.Is 58548 divisible by 9?
  31. 31.Is 98095 divisible by 15?
  32. 32.Is 20995 divisible by 13?
  33. 33.Is 27737 divisible by 7?
  34. 34.Is 50575 divisible by 17?
  35. 35.Is 1761 divisible by 2?
  36. 36.Is 20189 divisible by 13?
  37. 37.Is 7409 divisible by 11?
  38. 38.Is 58029 divisible by 23?
  39. 39.Is 85959 divisible by 24?
  40. 40.Is 9881 divisible by 24?

Answer key

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

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