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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 824 · 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 30130 divisible by 23?
  2. 2.Is 16736 divisible by 6?
  3. 3.Is 16515 divisible by 5?
  4. 4.Is 57606 divisible by 13?
  5. 5.Is 4605 divisible by 5?
  6. 6.Is 34644 divisible by 6?
  7. 7.Is 38966 divisible by 30?
  8. 8.Is 3273 divisible by 3?
  9. 9.Is 44760 divisible by 10?
  10. 10.Is 29464 divisible by 29?
  11. 11.Is 10684 divisible by 18?
  12. 12.Is 25782 divisible by 6?
  13. 13.Is 41293 divisible by 20?
  14. 14.Is 12185 divisible by 3?
  15. 15.Is 40113 divisible by 7?
  16. 16.Is 65642 divisible by 15?
  17. 17.Is 3651 divisible by 3?
  18. 18.Is 40824 divisible by 12?
  19. 19.Is 132965 divisible by 19?
  20. 20.Is 41429 divisible by 7?
  21. 21.Is 985 divisible by 4?
  22. 22.Is 85980 divisible by 30?
  23. 23.Is 126140 divisible by 20?
  24. 24.Is 1329 divisible by 4?
  25. 25.Is 156264 divisible by 24?
  26. 26.Is 6391 divisible by 7?
  27. 27.Is 113233 divisible by 20?
  28. 28.Is 3264 divisible by 24?
  29. 29.Is 7786 divisible by 5?
  30. 30.Is 20454 divisible by 7?
  31. 31.Is 83625 divisible by 13?
  32. 32.Is 37461 divisible by 10?
  33. 33.Is 41565 divisible by 8?
  34. 34.Is 24857 divisible by 15?
  35. 35.Is 2976 divisible by 8?
  36. 36.Is 9503 divisible by 2?
  37. 37.Is 40810 divisible by 7?
  38. 38.Is 121353 divisible by 19?
  39. 39.Is 2526 divisible by 2?
  40. 40.Is 8035 divisible by 2?

Answer key

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

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