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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 770 · 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 47862 divisible by 18?
  2. 2.Is 113120 divisible by 20?
  3. 3.Is 57366 divisible by 18?
  4. 4.Is 86228 divisible by 17?
  5. 5.Is 93195 divisible by 15?
  6. 6.Is 2721 divisible by 3?
  7. 7.Is 6783 divisible by 7?
  8. 8.Is 22486 divisible by 6?
  9. 9.Is 17736 divisible by 3?
  10. 10.Is 30907 divisible by 18?
  11. 11.Is 6633 divisible by 9?
  12. 12.Is 5392 divisible by 2?
  13. 13.Is 97312 divisible by 17?
  14. 14.Is 60676 divisible by 17?
  15. 15.Is 8063 divisible by 11?
  16. 16.Is 27240 divisible by 7?
  17. 17.Is 39028 divisible by 8?
  18. 18.Is 102472 divisible by 23?
  19. 19.Is 2138 divisible by 2?
  20. 20.Is 40246 divisible by 20?
  21. 21.Is 16992 divisible by 4?
  22. 22.Is 2912 divisible by 7?
  23. 23.Is 10123 divisible by 3?
  24. 24.Is 32922 divisible by 9?
  25. 25.Is 19084 divisible by 4?
  26. 26.Is 55536 divisible by 24?
  27. 27.Is 146266 divisible by 30?
  28. 28.Is 83579 divisible by 29?
  29. 29.Is 82348 divisible by 12?
  30. 30.Is 15514 divisible by 9?
  31. 31.Is 41269 divisible by 8?
  32. 32.Is 17710 divisible by 23?
  33. 33.Is 2848 divisible by 8?
  34. 34.Is 46550 divisible by 10?
  35. 35.Is 34757 divisible by 15?
  36. 36.Is 150330 divisible by 30?
  37. 37.Is 9926 divisible by 20?
  38. 38.Is 18352 divisible by 4?
  39. 39.Is 32296 divisible by 11?
  40. 40.Is 117635 divisible by 23?

Answer key

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

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