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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 224 · 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 8816 divisible by 3?
  2. 2.Is 61040 divisible by 12?
  3. 3.Is 13932 divisible by 3?
  4. 4.Is 3331 divisible by 2?
  5. 5.Is 26586 divisible by 7?
  6. 6.Is 27850 divisible by 8?
  7. 7.Is 34905 divisible by 29?
  8. 8.Is 59960 divisible by 29?
  9. 9.Is 304 divisible by 6?
  10. 10.Is 18264 divisible by 24?
  11. 11.Is 218 divisible by 3?
  12. 12.Is 28574 divisible by 7?
  13. 13.Is 10596 divisible by 3?
  14. 14.Is 17808 divisible by 8?
  15. 15.Is 99016 divisible by 18?
  16. 16.Is 4571 divisible by 3?
  17. 17.Is 13125 divisible by 20?
  18. 18.Is 47948 divisible by 30?
  19. 19.Is 157905 divisible by 29?
  20. 20.Is 27642 divisible by 5?
  21. 21.Is 10700 divisible by 20?
  22. 22.Is 8928 divisible by 18?
  23. 23.Is 41014 divisible by 19?
  24. 24.Is 2122 divisible by 12?
  25. 25.Is 33528 divisible by 24?
  26. 26.Is 11018 divisible by 9?
  27. 27.Is 36842 divisible by 6?
  28. 28.Is 23866 divisible by 15?
  29. 29.Is 169876 divisible by 30?
  30. 30.Is 105624 divisible by 18?
  31. 31.Is 83790 divisible by 15?
  32. 32.Is 34668 divisible by 9?
  33. 33.Is 161520 divisible by 24?
  34. 34.Is 90077 divisible by 13?
  35. 35.Is 49424 divisible by 8?
  36. 36.Is 210 divisible by 7?
  37. 37.Is 12393 divisible by 9?
  38. 38.Is 44479 divisible by 19?
  39. 39.Is 22080 divisible by 10?
  40. 40.Is 9036 divisible by 12?

Answer key

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

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