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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 875 · 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 39752 divisible by 9?
  2. 2.Is 21458 divisible by 24?
  3. 3.Is 123305 divisible by 30?
  4. 4.Is 84827 divisible by 15?
  5. 5.Is 107355 divisible by 17?
  6. 6.Is 185160 divisible by 30?
  7. 7.Is 14354 divisible by 23?
  8. 8.Is 115940 divisible by 17?
  9. 9.Is 27710 divisible by 5?
  10. 10.Is 37584 divisible by 18?
  11. 11.Is 92458 divisible by 15?
  12. 12.Is 180510 divisible by 30?
  13. 13.Is 25365 divisible by 4?
  14. 14.Is 5748 divisible by 4?
  15. 15.Is 106894 divisible by 29?
  16. 16.Is 2691 divisible by 6?
  17. 17.Is 56902 divisible by 23?
  18. 18.Is 17625 divisible by 15?
  19. 19.Is 30003 divisible by 29?
  20. 20.Is 4434 divisible by 29?
  21. 21.Is 24973 divisible by 13?
  22. 22.Is 154828 divisible by 29?
  23. 23.Is 46691 divisible by 9?
  24. 24.Is 62652 divisible by 12?
  25. 25.Is 15252 divisible by 12?
  26. 26.Is 72709 divisible by 13?
  27. 27.Is 13528 divisible by 17?
  28. 28.Is 199890 divisible by 30?
  29. 29.Is 3790 divisible by 3?
  30. 30.Is 52371 divisible by 23?
  31. 31.Is 15752 divisible by 18?
  32. 32.Is 54465 divisible by 17?
  33. 33.Is 6360 divisible by 30?
  34. 34.Is 29903 divisible by 7?
  35. 35.Is 35736 divisible by 13?
  36. 36.Is 62471 divisible by 11?
  37. 37.Is 8974 divisible by 2?
  38. 38.Is 9093 divisible by 6?
  39. 39.Is 28054 divisible by 5?
  40. 40.Is 69420 divisible by 30?

Answer key

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

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