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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 856 · 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 62681 divisible by 20?
  2. 2.Is 9474 divisible by 4?
  3. 3.Is 11612 divisible by 6?
  4. 4.Is 132960 divisible by 30?
  5. 5.Is 20965 divisible by 5?
  6. 6.Is 135592 divisible by 20?
  7. 7.Is 31763 divisible by 23?
  8. 8.Is 132434 divisible by 19?
  9. 9.Is 7920 divisible by 2?
  10. 10.Is 34047 divisible by 12?
  11. 11.Is 154584 divisible by 24?
  12. 12.Is 165555 divisible by 24?
  13. 13.Is 95816 divisible by 29?
  14. 14.Is 69117 divisible by 20?
  15. 15.Is 12430 divisible by 11?
  16. 16.Is 13195 divisible by 2?
  17. 17.Is 103701 divisible by 23?
  18. 18.Is 26910 divisible by 5?
  19. 19.Is 110640 divisible by 23?
  20. 20.Is 5331 divisible by 4?
  21. 21.Is 8578 divisible by 5?
  22. 22.Is 3089 divisible by 3?
  23. 23.Is 60885 divisible by 11?
  24. 24.Is 44700 divisible by 13?
  25. 25.Is 12410 divisible by 3?
  26. 26.Is 100269 divisible by 18?
  27. 27.Is 51980 divisible by 10?
  28. 28.Is 30482 divisible by 7?
  29. 29.Is 3033 divisible by 9?
  30. 30.Is 9605 divisible by 2?
  31. 31.Is 53887 divisible by 9?
  32. 32.Is 9554 divisible by 17?
  33. 33.Is 42977 divisible by 17?
  34. 34.Is 13658 divisible by 5?
  35. 35.Is 76562 divisible by 13?
  36. 36.Is 67668 divisible by 12?
  37. 37.Is 93381 divisible by 23?
  38. 38.Is 39997 divisible by 9?
  39. 39.Is 12743 divisible by 6?
  40. 40.Is 39120 divisible by 8?

Answer key

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

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