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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 916 · 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 9106 divisible by 5?
  2. 2.Is 99975 divisible by 15?
  3. 3.Is 85545 divisible by 30?
  4. 4.Is 122009 divisible by 23?
  5. 5.Is 19125 divisible by 9?
  6. 6.Is 94122 divisible by 18?
  7. 7.Is 55860 divisible by 12?
  8. 8.Is 9895 divisible by 5?
  9. 9.Is 36326 divisible by 15?
  10. 10.Is 43984 divisible by 8?
  11. 11.Is 10980 divisible by 30?
  12. 12.Is 12705 divisible by 2?
  13. 13.Is 1584 divisible by 10?
  14. 14.Is 8885 divisible by 2?
  15. 15.Is 13806 divisible by 6?
  16. 16.Is 132780 divisible by 20?
  17. 17.Is 96058 divisible by 24?
  18. 18.Is 185 divisible by 5?
  19. 19.Is 46371 divisible by 29?
  20. 20.Is 19935 divisible by 13?
  21. 21.Is 22330 divisible by 29?
  22. 22.Is 22795 divisible by 7?
  23. 23.Is 73493 divisible by 15?
  24. 24.Is 62784 divisible by 19?
  25. 25.Is 26010 divisible by 17?
  26. 26.Is 33860 divisible by 6?
  27. 27.Is 14840 divisible by 7?
  28. 28.Is 17322 divisible by 6?
  29. 29.Is 102653 divisible by 23?
  30. 30.Is 11135 divisible by 3?
  31. 31.Is 14020 divisible by 10?
  32. 32.Is 22758 divisible by 15?
  33. 33.Is 8234 divisible by 4?
  34. 34.Is 8028 divisible by 6?
  35. 35.Is 39712 divisible by 17?
  36. 36.Is 78117 divisible by 13?
  37. 37.Is 109017 divisible by 19?
  38. 38.Is 40935 divisible by 6?
  39. 39.Is 45124 divisible by 29?
  40. 40.Is 51091 divisible by 12?

Answer key

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

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