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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 859 · 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 45034 divisible by 11?
  2. 2.Is 48333 divisible by 9?
  3. 3.Is 8107 divisible by 8?
  4. 4.Is 38004 divisible by 23?
  5. 5.Is 30398 divisible by 7?
  6. 6.Is 16530 divisible by 3?
  7. 7.Is 75009 divisible by 24?
  8. 8.Is 99133 divisible by 15?
  9. 9.Is 23985 divisible by 15?
  10. 10.Is 42390 divisible by 15?
  11. 11.Is 32955 divisible by 7?
  12. 12.Is 180412 divisible by 30?
  13. 13.Is 57600 divisible by 15?
  14. 14.Is 27980 divisible by 20?
  15. 15.Is 13569 divisible by 2?
  16. 16.Is 33460 divisible by 6?
  17. 17.Is 184585 divisible by 29?
  18. 18.Is 106946 divisible by 19?
  19. 19.Is 140370 divisible by 30?
  20. 20.Is 63477 divisible by 23?
  21. 21.Is 1335 divisible by 5?
  22. 22.Is 54956 divisible by 8?
  23. 23.Is 50882 divisible by 13?
  24. 24.Is 48672 divisible by 12?
  25. 25.Is 5433 divisible by 6?
  26. 26.Is 71069 divisible by 17?
  27. 27.Is 45288 divisible by 24?
  28. 28.Is 52190 divisible by 10?
  29. 29.Is 15732 divisible by 19?
  30. 30.Is 16993 divisible by 12?
  31. 31.Is 49836 divisible by 12?
  32. 32.Is 3384 divisible by 24?
  33. 33.Is 24969 divisible by 19?
  34. 34.Is 127542 divisible by 29?
  35. 35.Is 20210 divisible by 6?
  36. 36.Is 42077 divisible by 7?
  37. 37.Is 5332 divisible by 3?
  38. 38.Is 129601 divisible by 29?
  39. 39.Is 20824 divisible by 8?
  40. 40.Is 30690 divisible by 5?

Answer key

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

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