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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 110 · 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 10886 divisible by 30?
  2. 2.Is 28052 divisible by 23?
  3. 3.Is 92790 divisible by 18?
  4. 4.Is 71880 divisible by 24?
  5. 5.Is 128260 divisible by 20?
  6. 6.Is 12700 divisible by 10?
  7. 7.Is 50357 divisible by 17?
  8. 8.Is 1147 divisible by 4?
  9. 9.Is 107020 divisible by 17?
  10. 10.Is 38332 divisible by 10?
  11. 11.Is 10976 divisible by 4?
  12. 12.Is 134885 divisible by 20?
  13. 13.Is 14640 divisible by 12?
  14. 14.Is 68709 divisible by 30?
  15. 15.Is 11200 divisible by 11?
  16. 16.Is 41972 divisible by 7?
  17. 17.Is 3905 divisible by 2?
  18. 18.Is 105067 divisible by 23?
  19. 19.Is 70499 divisible by 29?
  20. 20.Is 112272 divisible by 17?
  21. 21.Is 51377 divisible by 9?
  22. 22.Is 48714 divisible by 23?
  23. 23.Is 33908 divisible by 7?
  24. 24.Is 3199 divisible by 7?
  25. 25.Is 19552 divisible by 4?
  26. 26.Is 13892 divisible by 2?
  27. 27.Is 75649 divisible by 15?
  28. 28.Is 6651 divisible by 9?
  29. 29.Is 125889 divisible by 29?
  30. 30.Is 27982 divisible by 8?
  31. 31.Is 20818 divisible by 7?
  32. 32.Is 38341 divisible by 7?
  33. 33.Is 60444 divisible by 19?
  34. 34.Is 50819 divisible by 19?
  35. 35.Is 74639 divisible by 19?
  36. 36.Is 8304 divisible by 6?
  37. 37.Is 121040 divisible by 18?
  38. 38.Is 19188 divisible by 3?
  39. 39.Is 64447 divisible by 17?
  40. 40.Is 17933 divisible by 11?

Answer key

  1. no
  2. no
  3. yes
  4. yes
  5. yes
  6. yes
  7. no
  8. no
  9. no
  10. no
  11. yes
  12. no
  13. yes
  14. no
  15. no
  16. yes
  17. no
  18. no
  19. yes
  20. no
  21. no
  22. yes
  23. yes
  24. yes
  25. yes
  26. yes
  27. no
  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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