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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 292 · 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 5474 divisible by 9?
  2. 2.Is 12450 divisible by 30?
  3. 3.Is 61251 divisible by 19?
  4. 4.Is 47220 divisible by 9?
  5. 5.Is 88758 divisible by 18?
  6. 6.Is 93919 divisible by 29?
  7. 7.Is 35329 divisible by 7?
  8. 8.Is 42003 divisible by 13?
  9. 9.Is 10793 divisible by 2?
  10. 10.Is 27995 divisible by 5?
  11. 11.Is 23487 divisible by 4?
  12. 12.Is 88920 divisible by 18?
  13. 13.Is 100932 divisible by 19?
  14. 14.Is 76547 divisible by 23?
  15. 15.Is 35855 divisible by 7?
  16. 16.Is 10379 divisible by 6?
  17. 17.Is 23628 divisible by 4?
  18. 18.Is 58029 divisible by 29?
  19. 19.Is 27379 divisible by 15?
  20. 20.Is 183657 divisible by 29?
  21. 21.Is 8640 divisible by 3?
  22. 22.Is 38935 divisible by 8?
  23. 23.Is 7874 divisible by 3?
  24. 24.Is 64228 divisible by 13?
  25. 25.Is 19259 divisible by 15?
  26. 26.Is 25317 divisible by 29?
  27. 27.Is 29640 divisible by 20?
  28. 28.Is 12240 divisible by 6?
  29. 29.Is 19128 divisible by 6?
  30. 30.Is 36512 divisible by 6?
  31. 31.Is 18877 divisible by 3?
  32. 32.Is 5349 divisible by 2?
  33. 33.Is 2495 divisible by 5?
  34. 34.Is 2901 divisible by 4?
  35. 35.Is 59422 divisible by 9?
  36. 36.Is 20127 divisible by 6?
  37. 37.Is 34590 divisible by 10?
  38. 38.Is 24396 divisible by 12?
  39. 39.Is 5857 divisible by 4?
  40. 40.Is 8401 divisible by 6?

Answer key

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

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