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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 57 · 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 16890 divisible by 10?
  2. 2.Is 7401 divisible by 6?
  3. 3.Is 39877 divisible by 18?
  4. 4.Is 38360 divisible by 10?
  5. 5.Is 2690 divisible by 10?
  6. 6.Is 7799 divisible by 4?
  7. 7.Is 18116 divisible by 6?
  8. 8.Is 33230 divisible by 10?
  9. 9.Is 54084 divisible by 12?
  10. 10.Is 192960 divisible by 30?
  11. 11.Is 50605 divisible by 29?
  12. 12.Is 5504 divisible by 7?
  13. 13.Is 23195 divisible by 20?
  14. 14.Is 90403 divisible by 18?
  15. 15.Is 1173 divisible by 3?
  16. 16.Is 12274 divisible by 17?
  17. 17.Is 26145 divisible by 5?
  18. 18.Is 1882 divisible by 2?
  19. 19.Is 90120 divisible by 30?
  20. 20.Is 58212 divisible by 18?
  21. 21.Is 28485 divisible by 15?
  22. 22.Is 78588 divisible by 30?
  23. 23.Is 76196 divisible by 29?
  24. 24.Is 128820 divisible by 30?
  25. 25.Is 825 divisible by 5?
  26. 26.Is 1970 divisible by 5?
  27. 27.Is 22023 divisible by 9?
  28. 28.Is 46954 divisible by 19?
  29. 29.Is 42399 divisible by 9?
  30. 30.Is 10933 divisible by 29?
  31. 31.Is 105980 divisible by 20?
  32. 32.Is 3615 divisible by 4?
  33. 33.Is 5398 divisible by 13?
  34. 34.Is 29084 divisible by 10?
  35. 35.Is 637 divisible by 4?
  36. 36.Is 57694 divisible by 13?
  37. 37.Is 25437 divisible by 24?
  38. 38.Is 55679 divisible by 9?
  39. 39.Is 27019 divisible by 20?
  40. 40.Is 99774 divisible by 23?

Answer key

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

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