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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 431 · 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 118698 divisible by 23?
  2. 2.Is 8729 divisible by 20?
  3. 3.Is 55064 divisible by 20?
  4. 4.Is 83505 divisible by 15?
  5. 5.Is 506 divisible by 3?
  6. 6.Is 19156 divisible by 5?
  7. 7.Is 18803 divisible by 3?
  8. 8.Is 93195 divisible by 15?
  9. 9.Is 54750 divisible by 15?
  10. 10.Is 10155 divisible by 15?
  11. 11.Is 125438 divisible by 19?
  12. 12.Is 50565 divisible by 8?
  13. 13.Is 50083 divisible by 29?
  14. 14.Is 13145 divisible by 5?
  15. 15.Is 180004 divisible by 29?
  16. 16.Is 1031 divisible by 8?
  17. 17.Is 37050 divisible by 13?
  18. 18.Is 18025 divisible by 5?
  19. 19.Is 113885 divisible by 18?
  20. 20.Is 41875 divisible by 7?
  21. 21.Is 2986 divisible by 15?
  22. 22.Is 76967 divisible by 12?
  23. 23.Is 61830 divisible by 30?
  24. 24.Is 61492 divisible by 13?
  25. 25.Is 19903 divisible by 3?
  26. 26.Is 2626 divisible by 7?
  27. 27.Is 47830 divisible by 10?
  28. 28.Is 37610 divisible by 29?
  29. 29.Is 72202 divisible by 13?
  30. 30.Is 2958 divisible by 6?
  31. 31.Is 68928 divisible by 24?
  32. 32.Is 33271 divisible by 7?
  33. 33.Is 11637 divisible by 9?
  34. 34.Is 93704 divisible by 17?
  35. 35.Is 22430 divisible by 5?
  36. 36.Is 22299 divisible by 11?
  37. 37.Is 47176 divisible by 8?
  38. 38.Is 7951 divisible by 2?
  39. 39.Is 26413 divisible by 8?
  40. 40.Is 9290 divisible by 7?

Answer key

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

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