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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 657 · 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 59187 divisible by 13?
  2. 2.Is 24230 divisible by 24?
  3. 3.Is 87600 divisible by 24?
  4. 4.Is 28030 divisible by 5?
  5. 5.Is 30501 divisible by 9?
  6. 6.Is 19816 divisible by 3?
  7. 7.Is 7426 divisible by 4?
  8. 8.Is 87388 divisible by 20?
  9. 9.Is 10695 divisible by 5?
  10. 10.Is 37860 divisible by 6?
  11. 11.Is 33975 divisible by 5?
  12. 12.Is 30319 divisible by 13?
  13. 13.Is 113528 divisible by 23?
  14. 14.Is 174486 divisible by 29?
  15. 15.Is 55062 divisible by 23?
  16. 16.Is 2925 divisible by 13?
  17. 17.Is 35909 divisible by 10?
  18. 18.Is 11862 divisible by 6?
  19. 19.Is 31224 divisible by 8?
  20. 20.Is 21252 divisible by 23?
  21. 21.Is 12688 divisible by 4?
  22. 22.Is 29546 divisible by 7?
  23. 23.Is 44176 divisible by 10?
  24. 24.Is 13043 divisible by 4?
  25. 25.Is 4320 divisible by 15?
  26. 26.Is 148138 divisible by 29?
  27. 27.Is 7980 divisible by 12?
  28. 28.Is 102800 divisible by 20?
  29. 29.Is 8147 divisible by 15?
  30. 30.Is 13107 divisible by 13?
  31. 31.Is 21841 divisible by 6?
  32. 32.Is 54100 divisible by 20?
  33. 33.Is 17892 divisible by 7?
  34. 34.Is 105632 divisible by 23?
  35. 35.Is 23809 divisible by 7?
  36. 36.Is 58746 divisible by 11?
  37. 37.Is 78793 divisible by 13?
  38. 38.Is 20251 divisible by 11?
  39. 39.Is 6474 divisible by 4?
  40. 40.Is 38769 divisible by 8?

Answer key

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

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