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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 335 · 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 859 divisible by 13?
  2. 2.Is 120560 divisible by 29?
  3. 3.Is 117586 divisible by 23?
  4. 4.Is 30266 divisible by 12?
  5. 5.Is 35464 divisible by 12?
  6. 6.Is 140257 divisible by 24?
  7. 7.Is 19362 divisible by 6?
  8. 8.Is 29976 divisible by 8?
  9. 9.Is 111620 divisible by 19?
  10. 10.Is 24690 divisible by 15?
  11. 11.Is 43841 divisible by 23?
  12. 12.Is 48559 divisible by 7?
  13. 13.Is 22432 divisible by 4?
  14. 14.Is 87640 divisible by 20?
  15. 15.Is 117966 divisible by 18?
  16. 16.Is 17823 divisible by 3?
  17. 17.Is 9305 divisible by 5?
  18. 18.Is 163551 divisible by 24?
  19. 19.Is 9844 divisible by 2?
  20. 20.Is 652 divisible by 5?
  21. 21.Is 34530 divisible by 6?
  22. 22.Is 68460 divisible by 30?
  23. 23.Is 20856 divisible by 4?
  24. 24.Is 4130 divisible by 10?
  25. 25.Is 7210 divisible by 2?
  26. 26.Is 7851 divisible by 4?
  27. 27.Is 37565 divisible by 7?
  28. 28.Is 6060 divisible by 20?
  29. 29.Is 34690 divisible by 10?
  30. 30.Is 31905 divisible by 9?
  31. 31.Is 92092 divisible by 23?
  32. 32.Is 200880 divisible by 30?
  33. 33.Is 75106 divisible by 17?
  34. 34.Is 71711 divisible by 12?
  35. 35.Is 16437 divisible by 5?
  36. 36.Is 11709 divisible by 11?
  37. 37.Is 9720 divisible by 24?
  38. 38.Is 38076 divisible by 6?
  39. 39.Is 28928 divisible by 6?
  40. 40.Is 65544 divisible by 12?

Answer key

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

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