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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 769 · 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 82317 divisible by 23?
  2. 2.Is 84727 divisible by 15?
  3. 3.Is 52035 divisible by 10?
  4. 4.Is 46366 divisible by 20?
  5. 5.Is 5769 divisible by 3?
  6. 6.Is 9983 divisible by 7?
  7. 7.Is 131902 divisible by 20?
  8. 8.Is 172200 divisible by 30?
  9. 9.Is 30450 divisible by 8?
  10. 10.Is 12301 divisible by 15?
  11. 11.Is 33005 divisible by 5?
  12. 12.Is 66816 divisible by 19?
  13. 13.Is 32483 divisible by 6?
  14. 14.Is 127784 divisible by 19?
  15. 15.Is 159346 divisible by 24?
  16. 16.Is 14308 divisible by 9?
  17. 17.Is 47208 divisible by 18?
  18. 18.Is 84019 divisible by 23?
  19. 19.Is 8297 divisible by 4?
  20. 20.Is 43824 divisible by 24?
  21. 21.Is 28519 divisible by 19?
  22. 22.Is 34950 divisible by 15?
  23. 23.Is 25455 divisible by 9?
  24. 24.Is 35456 divisible by 20?
  25. 25.Is 7088 divisible by 3?
  26. 26.Is 128387 divisible by 19?
  27. 27.Is 59497 divisible by 15?
  28. 28.Is 26729 divisible by 18?
  29. 29.Is 41027 divisible by 10?
  30. 30.Is 79321 divisible by 29?
  31. 31.Is 27330 divisible by 8?
  32. 32.Is 41367 divisible by 6?
  33. 33.Is 3093 divisible by 2?
  34. 34.Is 1593 divisible by 3?
  35. 35.Is 24660 divisible by 18?
  36. 36.Is 8188 divisible by 2?
  37. 37.Is 19439 divisible by 24?
  38. 38.Is 10132 divisible by 6?
  39. 39.Is 99467 divisible by 15?
  40. 40.Is 10963 divisible by 19?

Answer key

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

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