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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 270 · 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 117461 divisible by 23?
  2. 2.Is 26446 divisible by 12?
  3. 3.Is 51992 divisible by 17?
  4. 4.Is 32187 divisible by 17?
  5. 5.Is 13740 divisible by 30?
  6. 6.Is 19816 divisible by 8?
  7. 7.Is 18542 divisible by 3?
  8. 8.Is 40757 divisible by 6?
  9. 9.Is 2233 divisible by 29?
  10. 10.Is 6511 divisible by 19?
  11. 11.Is 55998 divisible by 9?
  12. 12.Is 19453 divisible by 12?
  13. 13.Is 8575 divisible by 2?
  14. 14.Is 2340 divisible by 19?
  15. 15.Is 106508 divisible by 30?
  16. 16.Is 105756 divisible by 30?
  17. 17.Is 12457 divisible by 12?
  18. 18.Is 102120 divisible by 23?
  19. 19.Is 94572 divisible by 18?
  20. 20.Is 71693 divisible by 30?
  21. 21.Is 6298 divisible by 2?
  22. 22.Is 160575 divisible by 24?
  23. 23.Is 85552 divisible by 18?
  24. 24.Is 5250 divisible by 30?
  25. 25.Is 32879 divisible by 9?
  26. 26.Is 109204 divisible by 17?
  27. 27.Is 2133 divisible by 4?
  28. 28.Is 893 divisible by 9?
  29. 29.Is 80899 divisible by 13?
  30. 30.Is 121320 divisible by 24?
  31. 31.Is 12663 divisible by 9?
  32. 32.Is 36517 divisible by 6?
  33. 33.Is 14686 divisible by 6?
  34. 34.Is 29152 divisible by 13?
  35. 35.Is 156285 divisible by 23?
  36. 36.Is 30969 divisible by 9?
  37. 37.Is 19140 divisible by 3?
  38. 38.Is 83163 divisible by 24?
  39. 39.Is 1196 divisible by 23?
  40. 40.Is 53323 divisible by 15?

Answer key

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

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