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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 142 · 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 3981 divisible by 6?
  2. 2.Is 51435 divisible by 9?
  3. 3.Is 29134 divisible by 7?
  4. 4.Is 81205 divisible by 20?
  5. 5.Is 21869 divisible by 19?
  6. 6.Is 36204 divisible by 10?
  7. 7.Is 189299 divisible by 30?
  8. 8.Is 4024 divisible by 6?
  9. 9.Is 5397 divisible by 12?
  10. 10.Is 39451 divisible by 7?
  11. 11.Is 124654 divisible by 24?
  12. 12.Is 23062 divisible by 13?
  13. 13.Is 29049 divisible by 18?
  14. 14.Is 97966 divisible by 24?
  15. 15.Is 1466 divisible by 3?
  16. 16.Is 52223 divisible by 20?
  17. 17.Is 43202 divisible by 7?
  18. 18.Is 32565 divisible by 6?
  19. 19.Is 2968 divisible by 2?
  20. 20.Is 11735 divisible by 9?
  21. 21.Is 10526 divisible by 15?
  22. 22.Is 55418 divisible by 11?
  23. 23.Is 65558 divisible by 12?
  24. 24.Is 88111 divisible by 17?
  25. 25.Is 24048 divisible by 12?
  26. 26.Is 112070 divisible by 29?
  27. 27.Is 43482 divisible by 7?
  28. 28.Is 539 divisible by 2?
  29. 29.Is 11204 divisible by 7?
  30. 30.Is 23175 divisible by 13?
  31. 31.Is 359 divisible by 2?
  32. 32.Is 133124 divisible by 23?
  33. 33.Is 4836 divisible by 3?
  34. 34.Is 34980 divisible by 10?
  35. 35.Is 34418 divisible by 12?
  36. 36.Is 3556 divisible by 9?
  37. 37.Is 90496 divisible by 17?
  38. 38.Is 45816 divisible by 10?
  39. 39.Is 42230 divisible by 23?
  40. 40.Is 154077 divisible by 29?

Answer key

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

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