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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 815 · 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 31071 divisible by 12?
  2. 2.Is 11590 divisible by 10?
  3. 3.Is 92643 divisible by 20?
  4. 4.Is 14288 divisible by 19?
  5. 5.Is 93933 divisible by 23?
  6. 6.Is 118423 divisible by 23?
  7. 7.Is 73934 divisible by 20?
  8. 8.Is 41112 divisible by 8?
  9. 9.Is 40645 divisible by 8?
  10. 10.Is 30512 divisible by 15?
  11. 11.Is 107801 divisible by 23?
  12. 12.Is 119962 divisible by 18?
  13. 13.Is 31005 divisible by 9?
  14. 14.Is 57280 divisible by 20?
  15. 15.Is 11252 divisible by 9?
  16. 16.Is 50353 divisible by 9?
  17. 17.Is 121804 divisible by 24?
  18. 18.Is 9954 divisible by 2?
  19. 19.Is 145918 divisible by 30?
  20. 20.Is 12412 divisible by 6?
  21. 21.Is 33456 divisible by 6?
  22. 22.Is 63390 divisible by 23?
  23. 23.Is 4662 divisible by 6?
  24. 24.Is 53341 divisible by 12?
  25. 25.Is 47209 divisible by 17?
  26. 26.Is 12472 divisible by 2?
  27. 27.Is 24912 divisible by 8?
  28. 28.Is 18283 divisible by 8?
  29. 29.Is 78831 divisible by 19?
  30. 30.Is 43655 divisible by 15?
  31. 31.Is 63952 divisible by 13?
  32. 32.Is 98164 divisible by 23?
  33. 33.Is 13750 divisible by 6?
  34. 34.Is 39342 divisible by 6?
  35. 35.Is 32895 divisible by 9?
  36. 36.Is 25970 divisible by 5?
  37. 37.Is 2817 divisible by 7?
  38. 38.Is 108144 divisible by 18?
  39. 39.Is 9780 divisible by 3?
  40. 40.Is 7634 divisible by 24?

Answer key

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

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