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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 87 · 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 15407 divisible by 7?
  2. 2.Is 8254 divisible by 9?
  3. 3.Is 24221 divisible by 4?
  4. 4.Is 16634 divisible by 10?
  5. 5.Is 32981 divisible by 23?
  6. 6.Is 1482 divisible by 5?
  7. 7.Is 10302 divisible by 6?
  8. 8.Is 34727 divisible by 7?
  9. 9.Is 78286 divisible by 24?
  10. 10.Is 130594 divisible by 23?
  11. 11.Is 29394 divisible by 18?
  12. 12.Is 30714 divisible by 13?
  13. 13.Is 4528 divisible by 3?
  14. 14.Is 4426 divisible by 11?
  15. 15.Is 23016 divisible by 24?
  16. 16.Is 140133 divisible by 30?
  17. 17.Is 25347 divisible by 8?
  18. 18.Is 120916 divisible by 18?
  19. 19.Is 16499 divisible by 17?
  20. 20.Is 7514 divisible by 11?
  21. 21.Is 27704 divisible by 8?
  22. 22.Is 61920 divisible by 15?
  23. 23.Is 3168 divisible by 6?
  24. 24.Is 52982 divisible by 9?
  25. 25.Is 4911 divisible by 5?
  26. 26.Is 44281 divisible by 23?
  27. 27.Is 22540 divisible by 4?
  28. 28.Is 85663 divisible by 23?
  29. 29.Is 35285 divisible by 8?
  30. 30.Is 46290 divisible by 30?
  31. 31.Is 60360 divisible by 10?
  32. 32.Is 7198 divisible by 17?
  33. 33.Is 26868 divisible by 12?
  34. 34.Is 38696 divisible by 8?
  35. 35.Is 46395 divisible by 15?
  36. 36.Is 24652 divisible by 4?
  37. 37.Is 18144 divisible by 9?
  38. 38.Is 11580 divisible by 3?
  39. 39.Is 39510 divisible by 6?
  40. 40.Is 1054 divisible by 5?

Answer key

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

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