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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 76 · 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 55743 divisible by 17?
  2. 2.Is 15176 divisible by 13?
  3. 3.Is 70268 divisible by 24?
  4. 4.Is 63658 divisible by 17?
  5. 5.Is 11244 divisible by 13?
  6. 6.Is 30816 divisible by 12?
  7. 7.Is 11505 divisible by 6?
  8. 8.Is 68250 divisible by 13?
  9. 9.Is 9072 divisible by 3?
  10. 10.Is 165184 divisible by 29?
  11. 11.Is 4641 divisible by 17?
  12. 12.Is 5057 divisible by 13?
  13. 13.Is 5291 divisible by 11?
  14. 14.Is 1104 divisible by 23?
  15. 15.Is 25053 divisible by 5?
  16. 16.Is 38059 divisible by 10?
  17. 17.Is 945 divisible by 5?
  18. 18.Is 1033 divisible by 6?
  19. 19.Is 28683 divisible by 10?
  20. 20.Is 21576 divisible by 24?
  21. 21.Is 74124 divisible by 29?
  22. 22.Is 14896 divisible by 5?
  23. 23.Is 9647 divisible by 3?
  24. 24.Is 32582 divisible by 5?
  25. 25.Is 13533 divisible by 3?
  26. 26.Is 43078 divisible by 17?
  27. 27.Is 12529 divisible by 2?
  28. 28.Is 23430 divisible by 30?
  29. 29.Is 6604 divisible by 4?
  30. 30.Is 85289 divisible by 19?
  31. 31.Is 4963 divisible by 2?
  32. 32.Is 24350 divisible by 4?
  33. 33.Is 13486 divisible by 4?
  34. 34.Is 43605 divisible by 17?
  35. 35.Is 50103 divisible by 19?
  36. 36.Is 53749 divisible by 11?
  37. 37.Is 6164 divisible by 23?
  38. 38.Is 1992 divisible by 8?
  39. 39.Is 155516 divisible by 24?
  40. 40.Is 43785 divisible by 15?

Answer key

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

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