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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 541 · 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 19290 divisible by 15?
  2. 2.Is 7122 divisible by 2?
  3. 3.Is 1616 divisible by 8?
  4. 4.Is 105792 divisible by 29?
  5. 5.Is 85733 divisible by 15?
  6. 6.Is 6393 divisible by 2?
  7. 7.Is 12105 divisible by 2?
  8. 8.Is 16451 divisible by 24?
  9. 9.Is 17056 divisible by 20?
  10. 10.Is 74129 divisible by 12?
  11. 11.Is 11472 divisible by 12?
  12. 12.Is 11743 divisible by 7?
  13. 13.Is 19671 divisible by 3?
  14. 14.Is 10272 divisible by 8?
  15. 15.Is 85098 divisible by 13?
  16. 16.Is 163397 divisible by 24?
  17. 17.Is 33173 divisible by 7?
  18. 18.Is 11928 divisible by 6?
  19. 19.Is 23033 divisible by 29?
  20. 20.Is 855 divisible by 15?
  21. 21.Is 73680 divisible by 20?
  22. 22.Is 86972 divisible by 17?
  23. 23.Is 58305 divisible by 20?
  24. 24.Is 6153 divisible by 3?
  25. 25.Is 50373 divisible by 29?
  26. 26.Is 16546 divisible by 3?
  27. 27.Is 159571 divisible by 30?
  28. 28.Is 19993 divisible by 18?
  29. 29.Is 21078 divisible by 18?
  30. 30.Is 5605 divisible by 7?
  31. 31.Is 168577 divisible by 29?
  32. 32.Is 91680 divisible by 15?
  33. 33.Is 20607 divisible by 6?
  34. 34.Is 18520 divisible by 10?
  35. 35.Is 824 divisible by 8?
  36. 36.Is 3417 divisible by 2?
  37. 37.Is 143666 divisible by 29?
  38. 38.Is 34710 divisible by 13?
  39. 39.Is 20503 divisible by 3?
  40. 40.Is 51222 divisible by 11?

Answer key

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

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