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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 811 · 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 62761 divisible by 13?
  2. 2.Is 4784 divisible by 13?
  3. 3.Is 7665 divisible by 15?
  4. 4.Is 61125 divisible by 15?
  5. 5.Is 5381 divisible by 6?
  6. 6.Is 82314 divisible by 15?
  7. 7.Is 9765 divisible by 2?
  8. 8.Is 9319 divisible by 6?
  9. 9.Is 1632 divisible by 17?
  10. 10.Is 11072 divisible by 4?
  11. 11.Is 11999 divisible by 2?
  12. 12.Is 16054 divisible by 6?
  13. 13.Is 1189 divisible by 4?
  14. 14.Is 20864 divisible by 3?
  15. 15.Is 17499 divisible by 3?
  16. 16.Is 12510 divisible by 2?
  17. 17.Is 99104 divisible by 19?
  18. 18.Is 6745 divisible by 6?
  19. 19.Is 110615 divisible by 29?
  20. 20.Is 55312 divisible by 8?
  21. 21.Is 3997 divisible by 5?
  22. 22.Is 5575 divisible by 4?
  23. 23.Is 14448 divisible by 24?
  24. 24.Is 17373 divisible by 7?
  25. 25.Is 31359 divisible by 12?
  26. 26.Is 8144 divisible by 8?
  27. 27.Is 8027 divisible by 2?
  28. 28.Is 22455 divisible by 9?
  29. 29.Is 33939 divisible by 6?
  30. 30.Is 33889 divisible by 5?
  31. 31.Is 43061 divisible by 17?
  32. 32.Is 54750 divisible by 15?
  33. 33.Is 158597 divisible by 23?
  34. 34.Is 62928 divisible by 24?
  35. 35.Is 47717 divisible by 9?
  36. 36.Is 7658 divisible by 3?
  37. 37.Is 63346 divisible by 12?
  38. 38.Is 86879 divisible by 13?
  39. 39.Is 36232 divisible by 7?
  40. 40.Is 100027 divisible by 23?

Answer key

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

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