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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 464 · 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 45084 divisible by 13?
  2. 2.Is 10199 divisible by 6?
  3. 3.Is 7192 divisible by 2?
  4. 4.Is 8055 divisible by 7?
  5. 5.Is 24433 divisible by 30?
  6. 6.Is 41124 divisible by 6?
  7. 7.Is 22359 divisible by 17?
  8. 8.Is 59973 divisible by 12?
  9. 9.Is 24189 divisible by 11?
  10. 10.Is 15681 divisible by 4?
  11. 11.Is 3621 divisible by 3?
  12. 12.Is 53856 divisible by 11?
  13. 13.Is 12348 divisible by 6?
  14. 14.Is 27662 divisible by 15?
  15. 15.Is 14327 divisible by 7?
  16. 16.Is 22254 divisible by 6?
  17. 17.Is 73767 divisible by 23?
  18. 18.Is 84604 divisible by 13?
  19. 19.Is 29033 divisible by 5?
  20. 20.Is 25991 divisible by 7?
  21. 21.Is 41243 divisible by 7?
  22. 22.Is 59272 divisible by 9?
  23. 23.Is 9585 divisible by 5?
  24. 24.Is 9914 divisible by 2?
  25. 25.Is 37674 divisible by 7?
  26. 26.Is 34704 divisible by 20?
  27. 27.Is 27218 divisible by 7?
  28. 28.Is 16345 divisible by 3?
  29. 29.Is 38772 divisible by 9?
  30. 30.Is 19532 divisible by 12?
  31. 31.Is 67527 divisible by 12?
  32. 32.Is 57361 divisible by 19?
  33. 33.Is 30062 divisible by 7?
  34. 34.Is 32445 divisible by 9?
  35. 35.Is 39732 divisible by 11?
  36. 36.Is 107520 divisible by 20?
  37. 37.Is 13349 divisible by 5?
  38. 38.Is 25042 divisible by 4?
  39. 39.Is 58764 divisible by 19?
  40. 40.Is 15566 divisible by 6?

Answer key

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

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