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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 314 · 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 2767 divisible by 12?
  2. 2.Is 51502 divisible by 8?
  3. 3.Is 28067 divisible by 7?
  4. 4.Is 4710 divisible by 5?
  5. 5.Is 15420 divisible by 3?
  6. 6.Is 992 divisible by 4?
  7. 7.Is 33397 divisible by 24?
  8. 8.Is 113311 divisible by 23?
  9. 9.Is 71731 divisible by 15?
  10. 10.Is 47899 divisible by 7?
  11. 11.Is 28763 divisible by 13?
  12. 12.Is 12525 divisible by 3?
  13. 13.Is 156223 divisible by 29?
  14. 14.Is 149309 divisible by 23?
  15. 15.Is 5945 divisible by 5?
  16. 16.Is 4682 divisible by 2?
  17. 17.Is 12061 divisible by 2?
  18. 18.Is 185954 divisible by 30?
  19. 19.Is 77520 divisible by 17?
  20. 20.Is 4455 divisible by 5?
  21. 21.Is 37751 divisible by 7?
  22. 22.Is 8129 divisible by 5?
  23. 23.Is 21967 divisible by 15?
  24. 24.Is 12118 divisible by 8?
  25. 25.Is 20395 divisible by 15?
  26. 26.Is 6644 divisible by 2?
  27. 27.Is 34038 divisible by 6?
  28. 28.Is 68266 divisible by 11?
  29. 29.Is 7380 divisible by 12?
  30. 30.Is 58160 divisible by 10?
  31. 31.Is 6043 divisible by 6?
  32. 32.Is 2564 divisible by 20?
  33. 33.Is 2006 divisible by 6?
  34. 34.Is 196892 divisible by 30?
  35. 35.Is 35748 divisible by 18?
  36. 36.Is 99546 divisible by 23?
  37. 37.Is 12772 divisible by 4?
  38. 38.Is 6648 divisible by 6?
  39. 39.Is 45356 divisible by 29?
  40. 40.Is 117778 divisible by 17?

Answer key

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

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