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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 165 · 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 85441 divisible by 19?
  2. 2.Is 76350 divisible by 13?
  3. 3.Is 53713 divisible by 11?
  4. 4.Is 19464 divisible by 12?
  5. 5.Is 2424 divisible by 8?
  6. 6.Is 25305 divisible by 4?
  7. 7.Is 80406 divisible by 18?
  8. 8.Is 22698 divisible by 18?
  9. 9.Is 9116 divisible by 5?
  10. 10.Is 145245 divisible by 24?
  11. 11.Is 2085 divisible by 7?
  12. 12.Is 1764 divisible by 2?
  13. 13.Is 32113 divisible by 8?
  14. 14.Is 2952 divisible by 8?
  15. 15.Is 5238 divisible by 18?
  16. 16.Is 56806 divisible by 11?
  17. 17.Is 17484 divisible by 12?
  18. 18.Is 1055 divisible by 2?
  19. 19.Is 17667 divisible by 13?
  20. 20.Is 5652 divisible by 13?
  21. 21.Is 59787 divisible by 13?
  22. 22.Is 10472 divisible by 13?
  23. 23.Is 70330 divisible by 29?
  24. 24.Is 35330 divisible by 6?
  25. 25.Is 21835 divisible by 5?
  26. 26.Is 53243 divisible by 30?
  27. 27.Is 12978 divisible by 9?
  28. 28.Is 104797 divisible by 30?
  29. 29.Is 99891 divisible by 15?
  30. 30.Is 12504 divisible by 6?
  31. 31.Is 1661 divisible by 3?
  32. 32.Is 49130 divisible by 17?
  33. 33.Is 8179 divisible by 7?
  34. 34.Is 48927 divisible by 7?
  35. 35.Is 59643 divisible by 11?
  36. 36.Is 117287 divisible by 17?
  37. 37.Is 107677 divisible by 29?
  38. 38.Is 14731 divisible by 24?
  39. 39.Is 61590 divisible by 30?
  40. 40.Is 20652 divisible by 20?

Answer key

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

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