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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 60 · 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 99110 divisible by 17?
  2. 2.Is 15890 divisible by 6?
  3. 3.Is 38100 divisible by 20?
  4. 4.Is 27723 divisible by 4?
  5. 5.Is 156192 divisible by 24?
  6. 6.Is 42500 divisible by 10?
  7. 7.Is 134964 divisible by 30?
  8. 8.Is 102323 divisible by 17?
  9. 9.Is 34386 divisible by 7?
  10. 10.Is 56066 divisible by 24?
  11. 11.Is 20508 divisible by 6?
  12. 12.Is 9050 divisible by 8?
  13. 13.Is 4352 divisible by 4?
  14. 14.Is 121020 divisible by 24?
  15. 15.Is 5036 divisible by 3?
  16. 16.Is 33904 divisible by 13?
  17. 17.Is 6775 divisible by 5?
  18. 18.Is 77464 divisible by 23?
  19. 19.Is 2014 divisible by 10?
  20. 20.Is 684 divisible by 20?
  21. 21.Is 8600 divisible by 20?
  22. 22.Is 16574 divisible by 19?
  23. 23.Is 13584 divisible by 24?
  24. 24.Is 14795 divisible by 4?
  25. 25.Is 85722 divisible by 13?
  26. 26.Is 9521 divisible by 20?
  27. 27.Is 41814 divisible by 9?
  28. 28.Is 45110 divisible by 7?
  29. 29.Is 27610 divisible by 6?
  30. 30.Is 32136 divisible by 12?
  31. 31.Is 13552 divisible by 8?
  32. 32.Is 109180 divisible by 20?
  33. 33.Is 704 divisible by 4?
  34. 34.Is 57586 divisible by 11?
  35. 35.Is 22808 divisible by 6?
  36. 36.Is 113477 divisible by 29?
  37. 37.Is 7301 divisible by 7?
  38. 38.Is 25050 divisible by 30?
  39. 39.Is 3984 divisible by 24?
  40. 40.Is 102635 divisible by 23?

Answer key

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

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