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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 222 · 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 39067 divisible by 7?
  2. 2.Is 17005 divisible by 3?
  3. 3.Is 5293 divisible by 3?
  4. 4.Is 6417 divisible by 3?
  5. 5.Is 5406 divisible by 2?
  6. 6.Is 6688 divisible by 2?
  7. 7.Is 111826 divisible by 23?
  8. 8.Is 25404 divisible by 4?
  9. 9.Is 16380 divisible by 15?
  10. 10.Is 40434 divisible by 15?
  11. 11.Is 121377 divisible by 29?
  12. 12.Is 4561 divisible by 6?
  13. 13.Is 92951 divisible by 29?
  14. 14.Is 96750 divisible by 15?
  15. 15.Is 114081 divisible by 29?
  16. 16.Is 15270 divisible by 15?
  17. 17.Is 78455 divisible by 13?
  18. 18.Is 4113 divisible by 2?
  19. 19.Is 33633 divisible by 8?
  20. 20.Is 26340 divisible by 30?
  21. 21.Is 45847 divisible by 19?
  22. 22.Is 1273 divisible by 3?
  23. 23.Is 6181 divisible by 3?
  24. 24.Is 4440 divisible by 4?
  25. 25.Is 71688 divisible by 24?
  26. 26.Is 76821 divisible by 29?
  27. 27.Is 199399 divisible by 30?
  28. 28.Is 53070 divisible by 15?
  29. 29.Is 33771 divisible by 11?
  30. 30.Is 42975 divisible by 9?
  31. 31.Is 16926 divisible by 13?
  32. 32.Is 2718 divisible by 9?
  33. 33.Is 29472 divisible by 6?
  34. 34.Is 73109 divisible by 11?
  35. 35.Is 47957 divisible by 8?
  36. 36.Is 14153 divisible by 13?
  37. 37.Is 1073 divisible by 3?
  38. 38.Is 52064 divisible by 9?
  39. 39.Is 18813 divisible by 3?
  40. 40.Is 82550 divisible by 13?

Answer key

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

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