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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 580 · 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 130512 divisible by 19?
  2. 2.Is 29925 divisible by 7?
  3. 3.Is 47985 divisible by 23?
  4. 4.Is 3689 divisible by 5?
  5. 5.Is 8995 divisible by 2?
  6. 6.Is 137420 divisible by 20?
  7. 7.Is 68014 divisible by 10?
  8. 8.Is 80420 divisible by 20?
  9. 9.Is 105864 divisible by 24?
  10. 10.Is 6565 divisible by 3?
  11. 11.Is 28638 divisible by 30?
  12. 12.Is 142680 divisible by 29?
  13. 13.Is 5843 divisible by 5?
  14. 14.Is 55765 divisible by 19?
  15. 15.Is 36210 divisible by 30?
  16. 16.Is 20379 divisible by 6?
  17. 17.Is 44528 divisible by 23?
  18. 18.Is 18894 divisible by 6?
  19. 19.Is 94667 divisible by 20?
  20. 20.Is 44444 divisible by 19?
  21. 21.Is 32568 divisible by 23?
  22. 22.Is 24720 divisible by 4?
  23. 23.Is 16254 divisible by 9?
  24. 24.Is 31730 divisible by 15?
  25. 25.Is 88204 divisible by 17?
  26. 26.Is 50928 divisible by 12?
  27. 27.Is 13788 divisible by 3?
  28. 28.Is 13772 divisible by 17?
  29. 29.Is 37424 divisible by 7?
  30. 30.Is 8454 divisible by 3?
  31. 31.Is 6424 divisible by 8?
  32. 32.Is 10318 divisible by 11?
  33. 33.Is 153930 divisible by 30?
  34. 34.Is 14545 divisible by 23?
  35. 35.Is 10594 divisible by 6?
  36. 36.Is 71031 divisible by 13?
  37. 37.Is 29155 divisible by 17?
  38. 38.Is 14914 divisible by 4?
  39. 39.Is 96840 divisible by 18?
  40. 40.Is 14635 divisible by 5?

Answer key

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

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