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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 997 · 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 103851 divisible by 23?
  2. 2.Is 16791 divisible by 3?
  3. 3.Is 26593 divisible by 9?
  4. 4.Is 5693 divisible by 2?
  5. 5.Is 102809 divisible by 19?
  6. 6.Is 5855 divisible by 9?
  7. 7.Is 75677 divisible by 19?
  8. 8.Is 9221 divisible by 4?
  9. 9.Is 17992 divisible by 4?
  10. 10.Is 85352 divisible by 17?
  11. 11.Is 12099 divisible by 4?
  12. 12.Is 60600 divisible by 9?
  13. 13.Is 24456 divisible by 4?
  14. 14.Is 6108 divisible by 6?
  15. 15.Is 38538 divisible by 6?
  16. 16.Is 9793 divisible by 2?
  17. 17.Is 27940 divisible by 5?
  18. 18.Is 50849 divisible by 12?
  19. 19.Is 3567 divisible by 3?
  20. 20.Is 5393 divisible by 5?
  21. 21.Is 103637 divisible by 24?
  22. 22.Is 1167 divisible by 2?
  23. 23.Is 145122 divisible by 30?
  24. 24.Is 1710 divisible by 3?
  25. 25.Is 26912 divisible by 8?
  26. 26.Is 26450 divisible by 23?
  27. 27.Is 3671 divisible by 8?
  28. 28.Is 17791 divisible by 11?
  29. 29.Is 19768 divisible by 8?
  30. 30.Is 76832 divisible by 11?
  31. 31.Is 25410 divisible by 30?
  32. 32.Is 146328 divisible by 24?
  33. 33.Is 154566 divisible by 23?
  34. 34.Is 103052 divisible by 23?
  35. 35.Is 74015 divisible by 11?
  36. 36.Is 36946 divisible by 13?
  37. 37.Is 8840 divisible by 9?
  38. 38.Is 9037 divisible by 3?
  39. 39.Is 18552 divisible by 6?
  40. 40.Is 5285 divisible by 3?

Answer key

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

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