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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 408 · 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 4565 divisible by 5?
  2. 2.Is 61166 divisible by 17?
  3. 3.Is 8262 divisible by 17?
  4. 4.Is 4735 divisible by 7?
  5. 5.Is 49448 divisible by 8?
  6. 6.Is 3815 divisible by 8?
  7. 7.Is 104565 divisible by 15?
  8. 8.Is 97717 divisible by 23?
  9. 9.Is 51421 divisible by 15?
  10. 10.Is 4091 divisible by 8?
  11. 11.Is 12036 divisible by 2?
  12. 12.Is 155160 divisible by 24?
  13. 13.Is 59884 divisible by 19?
  14. 14.Is 62850 divisible by 10?
  15. 15.Is 34097 divisible by 15?
  16. 16.Is 129390 divisible by 24?
  17. 17.Is 7130 divisible by 23?
  18. 18.Is 76430 divisible by 24?
  19. 19.Is 9882 divisible by 9?
  20. 20.Is 34785 divisible by 5?
  21. 21.Is 75283 divisible by 13?
  22. 22.Is 6873 divisible by 29?
  23. 23.Is 16666 divisible by 13?
  24. 24.Is 69267 divisible by 11?
  25. 25.Is 7468 divisible by 2?
  26. 26.Is 17175 divisible by 12?
  27. 27.Is 7768 divisible by 5?
  28. 28.Is 82724 divisible by 23?
  29. 29.Is 87308 divisible by 20?
  30. 30.Is 12291 divisible by 17?
  31. 31.Is 62991 divisible by 13?
  32. 32.Is 30300 divisible by 15?
  33. 33.Is 2483 divisible by 3?
  34. 34.Is 44693 divisible by 17?
  35. 35.Is 30675 divisible by 5?
  36. 36.Is 17024 divisible by 3?
  37. 37.Is 51241 divisible by 13?
  38. 38.Is 17253 divisible by 3?
  39. 39.Is 32264 divisible by 24?
  40. 40.Is 3080 divisible by 20?

Answer key

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

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