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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 369 · 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 113900 divisible by 20?
  2. 2.Is 79830 divisible by 24?
  3. 3.Is 25329 divisible by 7?
  4. 4.Is 84 divisible by 2?
  5. 5.Is 10997 divisible by 7?
  6. 6.Is 25573 divisible by 6?
  7. 7.Is 96007 divisible by 23?
  8. 8.Is 208448 divisible by 30?
  9. 9.Is 58793 divisible by 24?
  10. 10.Is 81651 divisible by 17?
  11. 11.Is 43825 divisible by 30?
  12. 12.Is 122099 divisible by 30?
  13. 13.Is 6205 divisible by 5?
  14. 14.Is 64543 divisible by 19?
  15. 15.Is 5166 divisible by 18?
  16. 16.Is 119922 divisible by 23?
  17. 17.Is 8100 divisible by 30?
  18. 18.Is 2108 divisible by 17?
  19. 19.Is 15956 divisible by 4?
  20. 20.Is 20745 divisible by 5?
  21. 21.Is 17967 divisible by 4?
  22. 22.Is 12615 divisible by 29?
  23. 23.Is 5992 divisible by 7?
  24. 24.Is 28278 divisible by 18?
  25. 25.Is 1071 divisible by 5?
  26. 26.Is 2121 divisible by 6?
  27. 27.Is 32381 divisible by 7?
  28. 28.Is 95531 divisible by 23?
  29. 29.Is 48401 divisible by 29?
  30. 30.Is 117306 divisible by 19?
  31. 31.Is 27960 divisible by 11?
  32. 32.Is 30159 divisible by 5?
  33. 33.Is 24529 divisible by 24?
  34. 34.Is 10344 divisible by 4?
  35. 35.Is 58365 divisible by 15?
  36. 36.Is 7532 divisible by 4?
  37. 37.Is 3147 divisible by 2?
  38. 38.Is 139633 divisible by 23?
  39. 39.Is 13958 divisible by 2?
  40. 40.Is 71896 divisible by 11?

Answer key

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

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