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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 151 · 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 15380 divisible by 8?
  2. 2.Is 11827 divisible by 23?
  3. 3.Is 13979 divisible by 8?
  4. 4.Is 22284 divisible by 18?
  5. 5.Is 30689 divisible by 8?
  6. 6.Is 36652 divisible by 23?
  7. 7.Is 74990 divisible by 11?
  8. 8.Is 5447 divisible by 7?
  9. 9.Is 14923 divisible by 10?
  10. 10.Is 56181 divisible by 23?
  11. 11.Is 33426 divisible by 6?
  12. 12.Is 139654 divisible by 20?
  13. 13.Is 148259 divisible by 23?
  14. 14.Is 18637 divisible by 29?
  15. 15.Is 10714 divisible by 5?
  16. 16.Is 121920 divisible by 20?
  17. 17.Is 38670 divisible by 30?
  18. 18.Is 73467 divisible by 13?
  19. 19.Is 16715 divisible by 3?
  20. 20.Is 18112 divisible by 12?
  21. 21.Is 40132 divisible by 8?
  22. 22.Is 5968 divisible by 5?
  23. 23.Is 72750 divisible by 15?
  24. 24.Is 6732 divisible by 3?
  25. 25.Is 10478 divisible by 11?
  26. 26.Is 30876 divisible by 18?
  27. 27.Is 23668 divisible by 7?
  28. 28.Is 13634 divisible by 2?
  29. 29.Is 61332 divisible by 11?
  30. 30.Is 32293 divisible by 9?
  31. 31.Is 38437 divisible by 30?
  32. 32.Is 35812 divisible by 7?
  33. 33.Is 78447 divisible by 13?
  34. 34.Is 6401 divisible by 2?
  35. 35.Is 83733 divisible by 19?
  36. 36.Is 8207 divisible by 6?
  37. 37.Is 3558 divisible by 3?
  38. 38.Is 16272 divisible by 9?
  39. 39.Is 77123 divisible by 24?
  40. 40.Is 16992 divisible by 4?

Answer key

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

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