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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 518 · 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 14177 divisible by 19?
  2. 2.Is 6966 divisible by 6?
  3. 3.Is 31233 divisible by 5?
  4. 4.Is 34584 divisible by 5?
  5. 5.Is 11159 divisible by 4?
  6. 6.Is 45648 divisible by 9?
  7. 7.Is 36972 divisible by 13?
  8. 8.Is 88110 divisible by 15?
  9. 9.Is 10017 divisible by 3?
  10. 10.Is 25905 divisible by 15?
  11. 11.Is 17466 divisible by 7?
  12. 12.Is 913 divisible by 12?
  13. 13.Is 80779 divisible by 13?
  14. 14.Is 62938 divisible by 19?
  15. 15.Is 9352 divisible by 4?
  16. 16.Is 7314 divisible by 7?
  17. 17.Is 114120 divisible by 24?
  18. 18.Is 23545 divisible by 5?
  19. 19.Is 133008 divisible by 24?
  20. 20.Is 20126 divisible by 29?
  21. 21.Is 3955 divisible by 5?
  22. 22.Is 102871 divisible by 23?
  23. 23.Is 17852 divisible by 11?
  24. 24.Is 8857 divisible by 17?
  25. 25.Is 1813 divisible by 4?
  26. 26.Is 47270 divisible by 7?
  27. 27.Is 80143 divisible by 13?
  28. 28.Is 7196 divisible by 4?
  29. 29.Is 32031 divisible by 5?
  30. 30.Is 7119 divisible by 9?
  31. 31.Is 47980 divisible by 10?
  32. 32.Is 20432 divisible by 4?
  33. 33.Is 7501 divisible by 4?
  34. 34.Is 19020 divisible by 3?
  35. 35.Is 88044 divisible by 23?
  36. 36.Is 11585 divisible by 3?
  37. 37.Is 5368 divisible by 4?
  38. 38.Is 188951 divisible by 30?
  39. 39.Is 1570 divisible by 2?
  40. 40.Is 6814 divisible by 2?

Answer key

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

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