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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 668 · 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 73675 divisible by 13?
  2. 2.Is 16828 divisible by 13?
  3. 3.Is 97964 divisible by 29?
  4. 4.Is 40203 divisible by 7?
  5. 5.Is 32795 divisible by 5?
  6. 6.Is 46017 divisible by 17?
  7. 7.Is 37475 divisible by 24?
  8. 8.Is 11136 divisible by 4?
  9. 9.Is 92198 divisible by 19?
  10. 10.Is 25125 divisible by 6?
  11. 11.Is 19709 divisible by 3?
  12. 12.Is 147813 divisible by 24?
  13. 13.Is 72721 divisible by 11?
  14. 14.Is 7443 divisible by 2?
  15. 15.Is 118565 divisible by 23?
  16. 16.Is 15704 divisible by 4?
  17. 17.Is 4588 divisible by 12?
  18. 18.Is 9848 divisible by 4?
  19. 19.Is 46578 divisible by 17?
  20. 20.Is 15630 divisible by 15?
  21. 21.Is 38968 divisible by 7?
  22. 22.Is 18931 divisible by 4?
  23. 23.Is 51860 divisible by 18?
  24. 24.Is 47450 divisible by 13?
  25. 25.Is 92504 divisible by 18?
  26. 26.Is 39048 divisible by 8?
  27. 27.Is 36868 divisible by 13?
  28. 28.Is 26388 divisible by 6?
  29. 29.Is 12036 divisible by 6?
  30. 30.Is 43377 divisible by 19?
  31. 31.Is 9631 divisible by 6?
  32. 32.Is 142886 divisible by 23?
  33. 33.Is 11074 divisible by 8?
  34. 34.Is 16366 divisible by 7?
  35. 35.Is 88544 divisible by 18?
  36. 36.Is 11646 divisible by 3?
  37. 37.Is 9798 divisible by 2?
  38. 38.Is 20902 divisible by 9?
  39. 39.Is 16074 divisible by 18?
  40. 40.Is 83128 divisible by 18?

Answer key

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

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