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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 73 · 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 5845 divisible by 5?
  2. 2.Is 68832 divisible by 18?
  3. 3.Is 36102 divisible by 11?
  4. 4.Is 45270 divisible by 30?
  5. 5.Is 74233 divisible by 13?
  6. 6.Is 22855 divisible by 7?
  7. 7.Is 24955 divisible by 5?
  8. 8.Is 76505 divisible by 11?
  9. 9.Is 6864 divisible by 24?
  10. 10.Is 40013 divisible by 6?
  11. 11.Is 96120 divisible by 30?
  12. 12.Is 159252 divisible by 29?
  13. 13.Is 31646 divisible by 23?
  14. 14.Is 157 divisible by 10?
  15. 15.Is 1260 divisible by 30?
  16. 16.Is 8294 divisible by 6?
  17. 17.Is 2058 divisible by 2?
  18. 18.Is 58435 divisible by 29?
  19. 19.Is 15288 divisible by 6?
  20. 20.Is 86972 divisible by 17?
  21. 21.Is 27240 divisible by 10?
  22. 22.Is 37871 divisible by 18?
  23. 23.Is 47943 divisible by 8?
  24. 24.Is 87645 divisible by 20?
  25. 25.Is 15209 divisible by 23?
  26. 26.Is 9353 divisible by 6?
  27. 27.Is 31882 divisible by 19?
  28. 28.Is 7914 divisible by 6?
  29. 29.Is 36700 divisible by 20?
  30. 30.Is 3534 divisible by 2?
  31. 31.Is 40243 divisible by 6?
  32. 32.Is 10764 divisible by 12?
  33. 33.Is 9112 divisible by 4?
  34. 34.Is 9635 divisible by 13?
  35. 35.Is 38352 divisible by 24?
  36. 36.Is 31894 divisible by 17?
  37. 37.Is 37740 divisible by 6?
  38. 38.Is 3208 divisible by 6?
  39. 39.Is 29008 divisible by 7?
  40. 40.Is 14217 divisible by 8?

Answer key

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

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