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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 186 · 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 131073 divisible by 20?
  2. 2.Is 113732 divisible by 19?
  3. 3.Is 79956 divisible by 30?
  4. 4.Is 18563 divisible by 4?
  5. 5.Is 4697 divisible by 2?
  6. 6.Is 102885 divisible by 19?
  7. 7.Is 29594 divisible by 5?
  8. 8.Is 95039 divisible by 19?
  9. 9.Is 31125 divisible by 15?
  10. 10.Is 115647 divisible by 29?
  11. 11.Is 95374 divisible by 24?
  12. 12.Is 100234 divisible by 23?
  13. 13.Is 81115 divisible by 19?
  14. 14.Is 32896 divisible by 8?
  15. 15.Is 9531 divisible by 4?
  16. 16.Is 15525 divisible by 4?
  17. 17.Is 2808 divisible by 9?
  18. 18.Is 25980 divisible by 30?
  19. 19.Is 39842 divisible by 11?
  20. 20.Is 2331 divisible by 3?
  21. 21.Is 21633 divisible by 30?
  22. 22.Is 88866 divisible by 18?
  23. 23.Is 76199 divisible by 23?
  24. 24.Is 71088 divisible by 11?
  25. 25.Is 102147 divisible by 18?
  26. 26.Is 34437 divisible by 12?
  27. 27.Is 96620 divisible by 20?
  28. 28.Is 65537 divisible by 23?
  29. 29.Is 60296 divisible by 29?
  30. 30.Is 8232 divisible by 3?
  31. 31.Is 9482 divisible by 3?
  32. 32.Is 80267 divisible by 23?
  33. 33.Is 15659 divisible by 7?
  34. 34.Is 36346 divisible by 8?
  35. 35.Is 38571 divisible by 10?
  36. 36.Is 20009 divisible by 6?
  37. 37.Is 78409 divisible by 30?
  38. 38.Is 14007 divisible by 30?
  39. 39.Is 33516 divisible by 7?
  40. 40.Is 60159 divisible by 10?

Answer key

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

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