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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 99 · 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 44187 divisible by 23?
  2. 2.Is 135000 divisible by 24?
  3. 3.Is 513 divisible by 3?
  4. 4.Is 51880 divisible by 20?
  5. 5.Is 25504 divisible by 4?
  6. 6.Is 131005 divisible by 20?
  7. 7.Is 33196 divisible by 6?
  8. 8.Is 31399 divisible by 5?
  9. 9.Is 31614 divisible by 29?
  10. 10.Is 12104 divisible by 17?
  11. 11.Is 87933 divisible by 23?
  12. 12.Is 155460 divisible by 30?
  13. 13.Is 120251 divisible by 19?
  14. 14.Is 10754 divisible by 18?
  15. 15.Is 161906 divisible by 24?
  16. 16.Is 29405 divisible by 9?
  17. 17.Is 31800 divisible by 30?
  18. 18.Is 4792 divisible by 5?
  19. 19.Is 8107 divisible by 2?
  20. 20.Is 83188 divisible by 29?
  21. 21.Is 85680 divisible by 30?
  22. 22.Is 28359 divisible by 5?
  23. 23.Is 57480 divisible by 12?
  24. 24.Is 88941 divisible by 30?
  25. 25.Is 8409 divisible by 2?
  26. 26.Is 12164 divisible by 4?
  27. 27.Is 23083 divisible by 15?
  28. 28.Is 46935 divisible by 15?
  29. 29.Is 91910 divisible by 23?
  30. 30.Is 31391 divisible by 6?
  31. 31.Is 59121 divisible by 10?
  32. 32.Is 77622 divisible by 17?
  33. 33.Is 36703 divisible by 10?
  34. 34.Is 6389 divisible by 2?
  35. 35.Is 13677 divisible by 3?
  36. 36.Is 53504 divisible by 8?
  37. 37.Is 34483 divisible by 10?
  38. 38.Is 65067 divisible by 23?
  39. 39.Is 35887 divisible by 11?
  40. 40.Is 118522 divisible by 20?

Answer key

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

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