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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 20 · 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 10615 divisible by 11?
  2. 2.Is 56236 divisible by 17?
  3. 3.Is 100236 divisible by 30?
  4. 4.Is 115860 divisible by 30?
  5. 5.Is 42813 divisible by 9?
  6. 6.Is 193372 divisible by 29?
  7. 7.Is 29040 divisible by 5?
  8. 8.Is 96784 divisible by 23?
  9. 9.Is 18720 divisible by 12?
  10. 10.Is 2295 divisible by 30?
  11. 11.Is 59670 divisible by 17?
  12. 12.Is 27549 divisible by 4?
  13. 13.Is 153063 divisible by 29?
  14. 14.Is 11391 divisible by 3?
  15. 15.Is 21972 divisible by 12?
  16. 16.Is 60907 divisible by 11?
  17. 17.Is 21969 divisible by 4?
  18. 18.Is 25596 divisible by 6?
  19. 19.Is 21834 divisible by 11?
  20. 20.Is 4435 divisible by 5?
  21. 21.Is 126915 divisible by 20?
  22. 22.Is 16399 divisible by 3?
  23. 23.Is 27631 divisible by 18?
  24. 24.Is 17508 divisible by 6?
  25. 25.Is 35477 divisible by 13?
  26. 26.Is 123377 divisible by 23?
  27. 27.Is 4591 divisible by 2?
  28. 28.Is 10090 divisible by 3?
  29. 29.Is 4152 divisible by 12?
  30. 30.Is 5232 divisible by 4?
  31. 31.Is 40346 divisible by 8?
  32. 32.Is 4135 divisible by 6?
  33. 33.Is 82699 divisible by 13?
  34. 34.Is 27021 divisible by 6?
  35. 35.Is 142071 divisible by 29?
  36. 36.Is 18845 divisible by 4?
  37. 37.Is 13181 divisible by 8?
  38. 38.Is 45264 divisible by 12?
  39. 39.Is 23562 divisible by 12?
  40. 40.Is 6055 divisible by 7?

Answer key

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

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