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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 812 · 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 30980 divisible by 10?
  2. 2.Is 6498 divisible by 18?
  3. 3.Is 31470 divisible by 15?
  4. 4.Is 98190 divisible by 15?
  5. 5.Is 126393 divisible by 29?
  6. 6.Is 422 divisible by 3?
  7. 7.Is 93793 divisible by 29?
  8. 8.Is 82134 divisible by 18?
  9. 9.Is 106471 divisible by 17?
  10. 10.Is 1576 divisible by 11?
  11. 11.Is 3500 divisible by 4?
  12. 12.Is 39525 divisible by 11?
  13. 13.Is 37878 divisible by 6?
  14. 14.Is 8949 divisible by 19?
  15. 15.Is 64465 divisible by 19?
  16. 16.Is 11684 divisible by 5?
  17. 17.Is 4080 divisible by 2?
  18. 18.Is 22644 divisible by 17?
  19. 19.Is 5823 divisible by 9?
  20. 20.Is 9960 divisible by 8?
  21. 21.Is 7630 divisible by 5?
  22. 22.Is 61579 divisible by 19?
  23. 23.Is 143605 divisible by 29?
  24. 24.Is 69263 divisible by 20?
  25. 25.Is 125105 divisible by 23?
  26. 26.Is 144125 divisible by 24?
  27. 27.Is 33891 divisible by 13?
  28. 28.Is 101295 divisible by 15?
  29. 29.Is 4509 divisible by 12?
  30. 30.Is 99918 divisible by 18?
  31. 31.Is 23904 divisible by 12?
  32. 32.Is 115959 divisible by 20?
  33. 33.Is 12140 divisible by 10?
  34. 34.Is 769 divisible by 18?
  35. 35.Is 15939 divisible by 23?
  36. 36.Is 53332 divisible by 29?
  37. 37.Is 4583 divisible by 6?
  38. 38.Is 86362 divisible by 15?
  39. 39.Is 37472 divisible by 12?
  40. 40.Is 4554 divisible by 9?

Answer key

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

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