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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 724 · 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 45019 divisible by 29?
  2. 2.Is 5911 divisible by 11?
  3. 3.Is 138780 divisible by 30?
  4. 4.Is 30415 divisible by 11?
  5. 5.Is 17133 divisible by 23?
  6. 6.Is 55230 divisible by 30?
  7. 7.Is 56460 divisible by 30?
  8. 8.Is 19643 divisible by 7?
  9. 9.Is 2970 divisible by 4?
  10. 10.Is 93825 divisible by 15?
  11. 11.Is 56496 divisible by 11?
  12. 12.Is 23114 divisible by 5?
  13. 13.Is 64500 divisible by 18?
  14. 14.Is 11664 divisible by 18?
  15. 15.Is 1182 divisible by 3?
  16. 16.Is 14500 divisible by 4?
  17. 17.Is 1101 divisible by 8?
  18. 18.Is 83856 divisible by 12?
  19. 19.Is 27777 divisible by 8?
  20. 20.Is 11678 divisible by 3?
  21. 21.Is 35022 divisible by 7?
  22. 22.Is 9292 divisible by 13?
  23. 23.Is 24928 divisible by 19?
  24. 24.Is 76981 divisible by 23?
  25. 25.Is 28533 divisible by 7?
  26. 26.Is 36108 divisible by 17?
  27. 27.Is 19530 divisible by 5?
  28. 28.Is 28190 divisible by 5?
  29. 29.Is 9326 divisible by 9?
  30. 30.Is 4543 divisible by 7?
  31. 31.Is 22045 divisible by 5?
  32. 32.Is 13676 divisible by 5?
  33. 33.Is 43042 divisible by 7?
  34. 34.Is 12690 divisible by 6?
  35. 35.Is 13448 divisible by 8?
  36. 36.Is 3543 divisible by 2?
  37. 37.Is 25240 divisible by 5?
  38. 38.Is 9494 divisible by 3?
  39. 39.Is 44044 divisible by 11?
  40. 40.Is 59115 divisible by 15?

Answer key

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

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