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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 893 · 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 67440 divisible by 30?
  2. 2.Is 2821 divisible by 7?
  3. 3.Is 18153 divisible by 3?
  4. 4.Is 30787 divisible by 5?
  5. 5.Is 36172 divisible by 7?
  6. 6.Is 111853 divisible by 19?
  7. 7.Is 81360 divisible by 18?
  8. 8.Is 49592 divisible by 8?
  9. 9.Is 16184 divisible by 17?
  10. 10.Is 31175 divisible by 29?
  11. 11.Is 65829 divisible by 18?
  12. 12.Is 73242 divisible by 15?
  13. 13.Is 42354 divisible by 15?
  14. 14.Is 3113 divisible by 11?
  15. 15.Is 30690 divisible by 30?
  16. 16.Is 80702 divisible by 12?
  17. 17.Is 23513 divisible by 11?
  18. 18.Is 20998 divisible by 5?
  19. 19.Is 65477 divisible by 15?
  20. 20.Is 59819 divisible by 9?
  21. 21.Is 34327 divisible by 7?
  22. 22.Is 100055 divisible by 20?
  23. 23.Is 25294 divisible by 18?
  24. 24.Is 60072 divisible by 24?
  25. 25.Is 8564 divisible by 3?
  26. 26.Is 56166 divisible by 11?
  27. 27.Is 20860 divisible by 7?
  28. 28.Is 35637 divisible by 7?
  29. 29.Is 34539 divisible by 12?
  30. 30.Is 13398 divisible by 11?
  31. 31.Is 5260 divisible by 7?
  32. 32.Is 48571 divisible by 13?
  33. 33.Is 93563 divisible by 30?
  34. 34.Is 34139 divisible by 7?
  35. 35.Is 49402 divisible by 15?
  36. 36.Is 32425 divisible by 5?
  37. 37.Is 102336 divisible by 24?
  38. 38.Is 37032 divisible by 24?
  39. 39.Is 48437 divisible by 8?
  40. 40.Is 166620 divisible by 30?

Answer key

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

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