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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 908 · 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 11574 divisible by 4?
  2. 2.Is 116990 divisible by 30?
  3. 3.Is 31141 divisible by 11?
  4. 4.Is 11627 divisible by 7?
  5. 5.Is 69718 divisible by 23?
  6. 6.Is 44265 divisible by 13?
  7. 7.Is 4752 divisible by 3?
  8. 8.Is 108179 divisible by 18?
  9. 9.Is 100399 divisible by 15?
  10. 10.Is 140041 divisible by 24?
  11. 11.Is 38597 divisible by 6?
  12. 12.Is 63525 divisible by 23?
  13. 13.Is 3757 divisible by 3?
  14. 14.Is 58899 divisible by 29?
  15. 15.Is 189210 divisible by 30?
  16. 16.Is 65820 divisible by 15?
  17. 17.Is 20874 divisible by 6?
  18. 18.Is 55736 divisible by 8?
  19. 19.Is 5885 divisible by 8?
  20. 20.Is 69653 divisible by 24?
  21. 21.Is 15309 divisible by 3?
  22. 22.Is 14829 divisible by 3?
  23. 23.Is 4997 divisible by 3?
  24. 24.Is 19383 divisible by 13?
  25. 25.Is 9306 divisible by 18?
  26. 26.Is 2988 divisible by 7?
  27. 27.Is 31212 divisible by 6?
  28. 28.Is 32721 divisible by 19?
  29. 29.Is 11597 divisible by 7?
  30. 30.Is 6976 divisible by 2?
  31. 31.Is 22600 divisible by 7?
  32. 32.Is 14730 divisible by 7?
  33. 33.Is 6894 divisible by 6?
  34. 34.Is 20738 divisible by 19?
  35. 35.Is 63550 divisible by 10?
  36. 36.Is 30896 divisible by 23?
  37. 37.Is 45342 divisible by 9?
  38. 38.Is 145434 divisible by 24?
  39. 39.Is 3871 divisible by 6?
  40. 40.Is 2241 divisible by 7?

Answer key

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

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