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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 959 · 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 118523 divisible by 17?
  2. 2.Is 57760 divisible by 19?
  3. 3.Is 107485 divisible by 23?
  4. 4.Is 3544 divisible by 11?
  5. 5.Is 24615 divisible by 13?
  6. 6.Is 7342 divisible by 2?
  7. 7.Is 11019 divisible by 3?
  8. 8.Is 123623 divisible by 20?
  9. 9.Is 45376 divisible by 29?
  10. 10.Is 56795 divisible by 11?
  11. 11.Is 22854 divisible by 13?
  12. 12.Is 20006 divisible by 6?
  13. 13.Is 7944 divisible by 6?
  14. 14.Is 22252 divisible by 4?
  15. 15.Is 61443 divisible by 10?
  16. 16.Is 2712 divisible by 12?
  17. 17.Is 59079 divisible by 29?
  18. 18.Is 29673 divisible by 7?
  19. 19.Is 40143 divisible by 24?
  20. 20.Is 5280 divisible by 8?
  21. 21.Is 24885 divisible by 6?
  22. 22.Is 122635 divisible by 29?
  23. 23.Is 42559 divisible by 13?
  24. 24.Is 85606 divisible by 23?
  25. 25.Is 5619 divisible by 3?
  26. 26.Is 69520 divisible by 20?
  27. 27.Is 1328 divisible by 2?
  28. 28.Is 5492 divisible by 7?
  29. 29.Is 58075 divisible by 12?
  30. 30.Is 49236 divisible by 12?
  31. 31.Is 19294 divisible by 13?
  32. 32.Is 6403 divisible by 2?
  33. 33.Is 977 divisible by 2?
  34. 34.Is 31910 divisible by 5?
  35. 35.Is 16489 divisible by 15?
  36. 36.Is 9592 divisible by 6?
  37. 37.Is 32981 divisible by 13?
  38. 38.Is 13098 divisible by 6?
  39. 39.Is 679 divisible by 3?
  40. 40.Is 27193 divisible by 6?

Answer key

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

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