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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 885 · 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 139886 divisible by 23?
  2. 2.Is 25175 divisible by 11?
  3. 3.Is 17372 divisible by 23?
  4. 4.Is 12467 divisible by 7?
  5. 5.Is 14817 divisible by 5?
  6. 6.Is 22190 divisible by 10?
  7. 7.Is 52256 divisible by 8?
  8. 8.Is 51161 divisible by 18?
  9. 9.Is 33077 divisible by 7?
  10. 10.Is 28973 divisible by 7?
  11. 11.Is 143173 divisible by 29?
  12. 12.Is 2778 divisible by 5?
  13. 13.Is 10875 divisible by 5?
  14. 14.Is 13657 divisible by 4?
  15. 15.Is 85277 divisible by 13?
  16. 16.Is 60255 divisible by 13?
  17. 17.Is 2455 divisible by 5?
  18. 18.Is 74431 divisible by 13?
  19. 19.Is 10768 divisible by 30?
  20. 20.Is 24324 divisible by 6?
  21. 21.Is 6188 divisible by 7?
  22. 22.Is 38756 divisible by 20?
  23. 23.Is 6648 divisible by 8?
  24. 24.Is 19351 divisible by 9?
  25. 25.Is 35103 divisible by 23?
  26. 26.Is 41916 divisible by 12?
  27. 27.Is 31113 divisible by 15?
  28. 28.Is 7721 divisible by 4?
  29. 29.Is 197340 divisible by 30?
  30. 30.Is 27786 divisible by 7?
  31. 31.Is 22278 divisible by 6?
  32. 32.Is 104553 divisible by 17?
  33. 33.Is 86180 divisible by 20?
  34. 34.Is 41046 divisible by 7?
  35. 35.Is 26020 divisible by 20?
  36. 36.Is 110721 divisible by 17?
  37. 37.Is 27699 divisible by 8?
  38. 38.Is 7718 divisible by 4?
  39. 39.Is 36211 divisible by 7?
  40. 40.Is 43430 divisible by 11?

Answer key

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

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