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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 55 · 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 54819 divisible by 10?
  2. 2.Is 54208 divisible by 10?
  3. 3.Is 38881 divisible by 6?
  4. 4.Is 7142 divisible by 5?
  5. 5.Is 29645 divisible by 6?
  6. 6.Is 4366 divisible by 2?
  7. 7.Is 10791 divisible by 3?
  8. 8.Is 28890 divisible by 10?
  9. 9.Is 50726 divisible by 13?
  10. 10.Is 56637 divisible by 29?
  11. 11.Is 32900 divisible by 10?
  12. 12.Is 8063 divisible by 8?
  13. 13.Is 60697 divisible by 13?
  14. 14.Is 11539 divisible by 11?
  15. 15.Is 89428 divisible by 23?
  16. 16.Is 10857 divisible by 13?
  17. 17.Is 49658 divisible by 12?
  18. 18.Is 158250 divisible by 30?
  19. 19.Is 20370 divisible by 6?
  20. 20.Is 7174 divisible by 17?
  21. 21.Is 93540 divisible by 20?
  22. 22.Is 50640 divisible by 30?
  23. 23.Is 67183 divisible by 23?
  24. 24.Is 110700 divisible by 18?
  25. 25.Is 3929 divisible by 17?
  26. 26.Is 108019 divisible by 18?
  27. 27.Is 2568 divisible by 3?
  28. 28.Is 98928 divisible by 24?
  29. 29.Is 52392 divisible by 24?
  30. 30.Is 34260 divisible by 15?
  31. 31.Is 35052 divisible by 6?
  32. 32.Is 35914 divisible by 12?
  33. 33.Is 71216 divisible by 12?
  34. 34.Is 104063 divisible by 30?
  35. 35.Is 13665 divisible by 6?
  36. 36.Is 7924 divisible by 4?
  37. 37.Is 100422 divisible by 19?
  38. 38.Is 107015 divisible by 18?
  39. 39.Is 12438 divisible by 6?
  40. 40.Is 11591 divisible by 3?

Answer key

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

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