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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 149 · 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 45179 divisible by 13?
  2. 2.Is 12315 divisible by 6?
  3. 3.Is 27338 divisible by 5?
  4. 4.Is 12889 divisible by 29?
  5. 5.Is 47276 divisible by 29?
  6. 6.Is 6843 divisible by 4?
  7. 7.Is 51376 divisible by 8?
  8. 8.Is 105123 divisible by 24?
  9. 9.Is 92041 divisible by 15?
  10. 10.Is 110770 divisible by 24?
  11. 11.Is 60977 divisible by 10?
  12. 12.Is 113136 divisible by 24?
  13. 13.Is 5870 divisible by 10?
  14. 14.Is 71736 divisible by 12?
  15. 15.Is 28716 divisible by 12?
  16. 16.Is 47639 divisible by 30?
  17. 17.Is 4037 divisible by 5?
  18. 18.Is 35496 divisible by 8?
  19. 19.Is 18996 divisible by 12?
  20. 20.Is 63070 divisible by 17?
  21. 21.Is 18180 divisible by 15?
  22. 22.Is 15631 divisible by 5?
  23. 23.Is 56682 divisible by 9?
  24. 24.Is 81200 divisible by 29?
  25. 25.Is 13792 divisible by 8?
  26. 26.Is 80940 divisible by 20?
  27. 27.Is 8394 divisible by 3?
  28. 28.Is 5540 divisible by 10?
  29. 29.Is 107544 divisible by 24?
  30. 30.Is 144855 divisible by 29?
  31. 31.Is 14633 divisible by 4?
  32. 32.Is 26433 divisible by 9?
  33. 33.Is 82516 divisible by 13?
  34. 34.Is 3154 divisible by 4?
  35. 35.Is 14802 divisible by 3?
  36. 36.Is 11315 divisible by 6?
  37. 37.Is 13610 divisible by 4?
  38. 38.Is 14638 divisible by 12?
  39. 39.Is 17905 divisible by 6?
  40. 40.Is 9637 divisible by 4?

Answer key

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

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