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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 780 · 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 25434 divisible by 6?
  2. 2.Is 22024 divisible by 11?
  3. 3.Is 24957 divisible by 10?
  4. 4.Is 5267 divisible by 2?
  5. 5.Is 21042 divisible by 7?
  6. 6.Is 49005 divisible by 15?
  7. 7.Is 7354 divisible by 5?
  8. 8.Is 41473 divisible by 8?
  9. 9.Is 22170 divisible by 5?
  10. 10.Is 119628 divisible by 18?
  11. 11.Is 145889 divisible by 23?
  12. 12.Is 14605 divisible by 8?
  13. 13.Is 64227 divisible by 13?
  14. 14.Is 24037 divisible by 13?
  15. 15.Is 79413 divisible by 23?
  16. 16.Is 73780 divisible by 17?
  17. 17.Is 22680 divisible by 8?
  18. 18.Is 5598 divisible by 2?
  19. 19.Is 4116 divisible by 12?
  20. 20.Is 33005 divisible by 23?
  21. 21.Is 12896 divisible by 8?
  22. 22.Is 200782 divisible by 29?
  23. 23.Is 138215 divisible by 30?
  24. 24.Is 25923 divisible by 19?
  25. 25.Is 44966 divisible by 13?
  26. 26.Is 132886 divisible by 20?
  27. 27.Is 12675 divisible by 15?
  28. 28.Is 19626 divisible by 10?
  29. 29.Is 26235 divisible by 5?
  30. 30.Is 11137 divisible by 3?
  31. 31.Is 74951 divisible by 30?
  32. 32.Is 6004 divisible by 19?
  33. 33.Is 115711 divisible by 20?
  34. 34.Is 33598 divisible by 30?
  35. 35.Is 18755 divisible by 7?
  36. 36.Is 55788 divisible by 9?
  37. 37.Is 67222 divisible by 19?
  38. 38.Is 6651 divisible by 20?
  39. 39.Is 86147 divisible by 20?
  40. 40.Is 34110 divisible by 20?

Answer key

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

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