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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 608 · 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 18532 divisible by 5?
  2. 2.Is 17828 divisible by 13?
  3. 3.Is 40906 divisible by 8?
  4. 4.Is 26357 divisible by 29?
  5. 5.Is 29790 divisible by 18?
  6. 6.Is 23836 divisible by 4?
  7. 7.Is 87303 divisible by 24?
  8. 8.Is 9889 divisible by 11?
  9. 9.Is 16296 divisible by 4?
  10. 10.Is 1631 divisible by 15?
  11. 11.Is 16818 divisible by 6?
  12. 12.Is 1834 divisible by 3?
  13. 13.Is 98785 divisible by 17?
  14. 14.Is 8204 divisible by 7?
  15. 15.Is 16653 divisible by 7?
  16. 16.Is 5065 divisible by 9?
  17. 17.Is 17774 divisible by 12?
  18. 18.Is 2401 divisible by 7?
  19. 19.Is 34531 divisible by 5?
  20. 20.Is 65121 divisible by 29?
  21. 21.Is 41520 divisible by 12?
  22. 22.Is 66062 divisible by 29?
  23. 23.Is 104928 divisible by 24?
  24. 24.Is 54708 divisible by 12?
  25. 25.Is 27440 divisible by 19?
  26. 26.Is 12345 divisible by 2?
  27. 27.Is 9480 divisible by 19?
  28. 28.Is 78323 divisible by 19?
  29. 29.Is 24389 divisible by 29?
  30. 30.Is 80582 divisible by 30?
  31. 31.Is 26553 divisible by 7?
  32. 32.Is 44840 divisible by 10?
  33. 33.Is 11190 divisible by 10?
  34. 34.Is 97330 divisible by 23?
  35. 35.Is 43582 divisible by 7?
  36. 36.Is 177364 divisible by 29?
  37. 37.Is 37673 divisible by 6?
  38. 38.Is 51420 divisible by 30?
  39. 39.Is 15840 divisible by 11?
  40. 40.Is 177799 divisible by 29?

Answer key

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

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