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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 529 · 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 27313 divisible by 6?
  2. 2.Is 14919 divisible by 9?
  3. 3.Is 17301 divisible by 3?
  4. 4.Is 8420 divisible by 5?
  5. 5.Is 10785 divisible by 2?
  6. 6.Is 67923 divisible by 10?
  7. 7.Is 81844 divisible by 17?
  8. 8.Is 14399 divisible by 3?
  9. 9.Is 22505 divisible by 7?
  10. 10.Is 122246 divisible by 19?
  11. 11.Is 88426 divisible by 13?
  12. 12.Is 10898 divisible by 9?
  13. 13.Is 17533 divisible by 3?
  14. 14.Is 22509 divisible by 30?
  15. 15.Is 85514 divisible by 13?
  16. 16.Is 14917 divisible by 19?
  17. 17.Is 149808 divisible by 24?
  18. 18.Is 32130 divisible by 7?
  19. 19.Is 56818 divisible by 23?
  20. 20.Is 53608 divisible by 8?
  21. 21.Is 77910 divisible by 30?
  22. 22.Is 37549 divisible by 9?
  23. 23.Is 93336 divisible by 24?
  24. 24.Is 76502 divisible by 29?
  25. 25.Is 26132 divisible by 12?
  26. 26.Is 29379 divisible by 7?
  27. 27.Is 22121 divisible by 11?
  28. 28.Is 60178 divisible by 19?
  29. 29.Is 33663 divisible by 19?
  30. 30.Is 77555 divisible by 13?
  31. 31.Is 38460 divisible by 6?
  32. 32.Is 148480 divisible by 29?
  33. 33.Is 18966 divisible by 4?
  34. 34.Is 121488 divisible by 24?
  35. 35.Is 37621 divisible by 17?
  36. 36.Is 70224 divisible by 11?
  37. 37.Is 9736 divisible by 13?
  38. 38.Is 29802 divisible by 9?
  39. 39.Is 8606 divisible by 4?
  40. 40.Is 7135 divisible by 9?

Answer key

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

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