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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 568 · 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 7417 divisible by 3?
  2. 2.Is 92212 divisible by 29?
  3. 3.Is 154882 divisible by 29?
  4. 4.Is 17618 divisible by 15?
  5. 5.Is 34242 divisible by 5?
  6. 6.Is 13466 divisible by 5?
  7. 7.Is 119585 divisible by 23?
  8. 8.Is 26528 divisible by 4?
  9. 9.Is 30455 divisible by 15?
  10. 10.Is 97614 divisible by 17?
  11. 11.Is 59199 divisible by 23?
  12. 12.Is 2728 divisible by 8?
  13. 13.Is 4466 divisible by 29?
  14. 14.Is 3245 divisible by 11?
  15. 15.Is 108995 divisible by 20?
  16. 16.Is 194580 divisible by 30?
  17. 17.Is 28400 divisible by 5?
  18. 18.Is 90552 divisible by 24?
  19. 19.Is 59442 divisible by 10?
  20. 20.Is 54522 divisible by 13?
  21. 21.Is 4215 divisible by 30?
  22. 22.Is 43368 divisible by 8?
  23. 23.Is 35483 divisible by 11?
  24. 24.Is 46721 divisible by 19?
  25. 25.Is 51760 divisible by 20?
  26. 26.Is 8258 divisible by 7?
  27. 27.Is 39636 divisible by 6?
  28. 28.Is 9389 divisible by 9?
  29. 29.Is 15694 divisible by 8?
  30. 30.Is 183761 divisible by 30?
  31. 31.Is 44740 divisible by 10?
  32. 32.Is 6600 divisible by 20?
  33. 33.Is 5744 divisible by 2?
  34. 34.Is 165012 divisible by 24?
  35. 35.Is 12835 divisible by 5?
  36. 36.Is 22774 divisible by 8?
  37. 37.Is 41808 divisible by 12?
  38. 38.Is 34772 divisible by 5?
  39. 39.Is 7518 divisible by 7?
  40. 40.Is 16572 divisible by 8?

Answer key

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

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