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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 409 · 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 10540 divisible by 2?
  2. 2.Is 50944 divisible by 8?
  3. 3.Is 2556 divisible by 2?
  4. 4.Is 4650 divisible by 3?
  5. 5.Is 27959 divisible by 11?
  6. 6.Is 127022 divisible by 29?
  7. 7.Is 59686 divisible by 11?
  8. 8.Is 62002 divisible by 12?
  9. 9.Is 62950 divisible by 20?
  10. 10.Is 15843 divisible by 5?
  11. 11.Is 112055 divisible by 30?
  12. 12.Is 134044 divisible by 23?
  13. 13.Is 22114 divisible by 20?
  14. 14.Is 8566 divisible by 7?
  15. 15.Is 21659 divisible by 6?
  16. 16.Is 172434 divisible by 29?
  17. 17.Is 32705 divisible by 5?
  18. 18.Is 40461 divisible by 8?
  19. 19.Is 49665 divisible by 11?
  20. 20.Is 183780 divisible by 30?
  21. 21.Is 93785 divisible by 19?
  22. 22.Is 79152 divisible by 17?
  23. 23.Is 3915 divisible by 2?
  24. 24.Is 19285 divisible by 17?
  25. 25.Is 25420 divisible by 10?
  26. 26.Is 99065 divisible by 20?
  27. 27.Is 16079 divisible by 7?
  28. 28.Is 5817 divisible by 6?
  29. 29.Is 2941 divisible by 17?
  30. 30.Is 114102 divisible by 18?
  31. 31.Is 54502 divisible by 10?
  32. 32.Is 34401 divisible by 11?
  33. 33.Is 19997 divisible by 4?
  34. 34.Is 73792 divisible by 23?
  35. 35.Is 103230 divisible by 18?
  36. 36.Is 5274 divisible by 19?
  37. 37.Is 4362 divisible by 6?
  38. 38.Is 29873 divisible by 6?
  39. 39.Is 40641 divisible by 19?
  40. 40.Is 93974 divisible by 19?

Answer key

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

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