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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 597 · 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 9300 divisible by 2?
  2. 2.Is 11610 divisible by 5?
  3. 3.Is 31020 divisible by 5?
  4. 4.Is 11530 divisible by 17?
  5. 5.Is 75145 divisible by 19?
  6. 6.Is 105909 divisible by 17?
  7. 7.Is 1455 divisible by 5?
  8. 8.Is 91035 divisible by 20?
  9. 9.Is 132000 divisible by 24?
  10. 10.Is 6305 divisible by 2?
  11. 11.Is 4757 divisible by 2?
  12. 12.Is 37693 divisible by 20?
  13. 13.Is 51891 divisible by 8?
  14. 14.Is 2362 divisible by 4?
  15. 15.Is 12248 divisible by 4?
  16. 16.Is 12656 divisible by 7?
  17. 17.Is 13244 divisible by 11?
  18. 18.Is 136 divisible by 8?
  19. 19.Is 2790 divisible by 18?
  20. 20.Is 56310 divisible by 30?
  21. 21.Is 22496 divisible by 7?
  22. 22.Is 2904 divisible by 11?
  23. 23.Is 30317 divisible by 6?
  24. 24.Is 41423 divisible by 7?
  25. 25.Is 351 divisible by 7?
  26. 26.Is 126882 divisible by 19?
  27. 27.Is 111912 divisible by 24?
  28. 28.Is 25799 divisible by 7?
  29. 29.Is 163272 divisible by 24?
  30. 30.Is 57114 divisible by 19?
  31. 31.Is 5207 divisible by 3?
  32. 32.Is 72180 divisible by 18?
  33. 33.Is 29287 divisible by 24?
  34. 34.Is 32591 divisible by 23?
  35. 35.Is 138460 divisible by 23?
  36. 36.Is 33315 divisible by 13?
  37. 37.Is 14450 divisible by 6?
  38. 38.Is 2662 divisible by 2?
  39. 39.Is 10185 divisible by 15?
  40. 40.Is 93260 divisible by 20?

Answer key

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

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