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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 862 · 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 25611 divisible by 17?
  2. 2.Is 21087 divisible by 11?
  3. 3.Is 78693 divisible by 12?
  4. 4.Is 37812 divisible by 15?
  5. 5.Is 7470 divisible by 2?
  6. 6.Is 4881 divisible by 8?
  7. 7.Is 70176 divisible by 17?
  8. 8.Is 10303 divisible by 2?
  9. 9.Is 49128 divisible by 8?
  10. 10.Is 43095 divisible by 17?
  11. 11.Is 94316 divisible by 19?
  12. 12.Is 133906 divisible by 23?
  13. 13.Is 37329 divisible by 29?
  14. 14.Is 58082 divisible by 30?
  15. 15.Is 45315 divisible by 19?
  16. 16.Is 29559 divisible by 7?
  17. 17.Is 24796 divisible by 5?
  18. 18.Is 21160 divisible by 5?
  19. 19.Is 47686 divisible by 8?
  20. 20.Is 13226 divisible by 3?
  21. 21.Is 112224 divisible by 20?
  22. 22.Is 153134 divisible by 23?
  23. 23.Is 34856 divisible by 12?
  24. 24.Is 82586 divisible by 17?
  25. 25.Is 15649 divisible by 8?
  26. 26.Is 83682 divisible by 23?
  27. 27.Is 12716 divisible by 13?
  28. 28.Is 655 divisible by 2?
  29. 29.Is 18525 divisible by 10?
  30. 30.Is 204638 divisible by 30?
  31. 31.Is 135870 divisible by 30?
  32. 32.Is 424 divisible by 5?
  33. 33.Is 478 divisible by 3?
  34. 34.Is 7094 divisible by 3?
  35. 35.Is 155665 divisible by 24?
  36. 36.Is 46880 divisible by 17?
  37. 37.Is 98285 divisible by 19?
  38. 38.Is 120168 divisible by 18?
  39. 39.Is 51915 divisible by 30?
  40. 40.Is 2870 divisible by 7?

Answer key

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

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