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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 984 · 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 36963 divisible by 17?
  2. 2.Is 163950 divisible by 30?
  3. 3.Is 83720 divisible by 20?
  4. 4.Is 38879 divisible by 10?
  5. 5.Is 14220 divisible by 12?
  6. 6.Is 24038 divisible by 17?
  7. 7.Is 45513 divisible by 7?
  8. 8.Is 47490 divisible by 30?
  9. 9.Is 130364 divisible by 23?
  10. 10.Is 11818 divisible by 3?
  11. 11.Is 98256 divisible by 24?
  12. 12.Is 16456 divisible by 17?
  13. 13.Is 6760 divisible by 3?
  14. 14.Is 67994 divisible by 13?
  15. 15.Is 25272 divisible by 12?
  16. 16.Is 12955 divisible by 12?
  17. 17.Is 58353 divisible by 24?
  18. 18.Is 1798 divisible by 29?
  19. 19.Is 7192 divisible by 4?
  20. 20.Is 62640 divisible by 20?
  21. 21.Is 87480 divisible by 18?
  22. 22.Is 71519 divisible by 13?
  23. 23.Is 50342 divisible by 24?
  24. 24.Is 64056 divisible by 12?
  25. 25.Is 157656 divisible by 24?
  26. 26.Is 32430 divisible by 6?
  27. 27.Is 42744 divisible by 24?
  28. 28.Is 2880 divisible by 8?
  29. 29.Is 20336 divisible by 3?
  30. 30.Is 60799 divisible by 10?
  31. 31.Is 27980 divisible by 4?
  32. 32.Is 34434 divisible by 18?
  33. 33.Is 35383 divisible by 6?
  34. 34.Is 31234 divisible by 23?
  35. 35.Is 50448 divisible by 8?
  36. 36.Is 107424 divisible by 24?
  37. 37.Is 9691 divisible by 4?
  38. 38.Is 12966 divisible by 7?
  39. 39.Is 127800 divisible by 24?
  40. 40.Is 100091 divisible by 29?

Answer key

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

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