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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 281 · 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 76435 divisible by 18?
  2. 2.Is 35128 divisible by 8?
  3. 3.Is 28644 divisible by 12?
  4. 4.Is 41623 divisible by 7?
  5. 5.Is 78646 divisible by 17?
  6. 6.Is 35924 divisible by 23?
  7. 7.Is 53760 divisible by 10?
  8. 8.Is 1482 divisible by 6?
  9. 9.Is 17999 divisible by 11?
  10. 10.Is 26660 divisible by 12?
  11. 11.Is 55893 divisible by 10?
  12. 12.Is 16632 divisible by 12?
  13. 13.Is 22162 divisible by 13?
  14. 14.Is 45043 divisible by 13?
  15. 15.Is 66529 divisible by 24?
  16. 16.Is 13355 divisible by 7?
  17. 17.Is 44751 divisible by 7?
  18. 18.Is 22122 divisible by 12?
  19. 19.Is 48456 divisible by 24?
  20. 20.Is 26225 divisible by 5?
  21. 21.Is 39109 divisible by 18?
  22. 22.Is 198694 divisible by 30?
  23. 23.Is 3077 divisible by 20?
  24. 24.Is 8833 divisible by 4?
  25. 25.Is 17745 divisible by 5?
  26. 26.Is 919 divisible by 3?
  27. 27.Is 2910 divisible by 30?
  28. 28.Is 88830 divisible by 18?
  29. 29.Is 155687 divisible by 23?
  30. 30.Is 54972 divisible by 9?
  31. 31.Is 6390 divisible by 10?
  32. 32.Is 25880 divisible by 20?
  33. 33.Is 40434 divisible by 6?
  34. 34.Is 5893 divisible by 2?
  35. 35.Is 3502 divisible by 3?
  36. 36.Is 202758 divisible by 29?
  37. 37.Is 73067 divisible by 11?
  38. 38.Is 75188 divisible by 17?
  39. 39.Is 17446 divisible by 10?
  40. 40.Is 23330 divisible by 10?

Answer key

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

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