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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 573 · 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 74878 divisible by 29?
  2. 2.Is 4711 divisible by 7?
  3. 3.Is 12333 divisible by 10?
  4. 4.Is 77352 divisible by 12?
  5. 5.Is 6616 divisible by 4?
  6. 6.Is 76558 divisible by 17?
  7. 7.Is 29854 divisible by 5?
  8. 8.Is 16841 divisible by 6?
  9. 9.Is 11832 divisible by 17?
  10. 10.Is 35184 divisible by 24?
  11. 11.Is 7289 divisible by 18?
  12. 12.Is 93311 divisible by 23?
  13. 13.Is 11236 divisible by 18?
  14. 14.Is 61660 divisible by 17?
  15. 15.Is 26876 divisible by 23?
  16. 16.Is 99139 divisible by 17?
  17. 17.Is 71832 divisible by 12?
  18. 18.Is 1574 divisible by 5?
  19. 19.Is 6371 divisible by 2?
  20. 20.Is 4585 divisible by 7?
  21. 21.Is 9320 divisible by 10?
  22. 22.Is 54618 divisible by 13?
  23. 23.Is 30107 divisible by 15?
  24. 24.Is 54365 divisible by 29?
  25. 25.Is 2015 divisible by 5?
  26. 26.Is 87841 divisible by 29?
  27. 27.Is 118356 divisible by 24?
  28. 28.Is 91372 divisible by 24?
  29. 29.Is 3260 divisible by 11?
  30. 30.Is 872 divisible by 17?
  31. 31.Is 64012 divisible by 10?
  32. 32.Is 35220 divisible by 30?
  33. 33.Is 116939 divisible by 19?
  34. 34.Is 29582 divisible by 7?
  35. 35.Is 7400 divisible by 10?
  36. 36.Is 66407 divisible by 11?
  37. 37.Is 20111 divisible by 17?
  38. 38.Is 37269 divisible by 9?
  39. 39.Is 1710 divisible by 15?
  40. 40.Is 31961 divisible by 9?

Answer key

  1. yes
  2. yes
  3. no
  4. yes
  5. yes
  6. no
  7. no
  8. no
  9. yes
  10. yes
  11. no
  12. yes
  13. no
  14. no
  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. no
  29. no
  30. no
  31. no
  32. yes
  33. no
  34. yes
  35. yes
  36. yes
  37. yes
  38. yes
  39. yes
  40. no

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