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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 176 · 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 25794 divisible by 7?
  2. 2.Is 165793 divisible by 29?
  3. 3.Is 23089 divisible by 11?
  4. 4.Is 32148 divisible by 12?
  5. 5.Is 62301 divisible by 17?
  6. 6.Is 46858 divisible by 19?
  7. 7.Is 1263 divisible by 11?
  8. 8.Is 1974 divisible by 6?
  9. 9.Is 8969 divisible by 7?
  10. 10.Is 45138 divisible by 19?
  11. 11.Is 2220 divisible by 2?
  12. 12.Is 29144 divisible by 6?
  13. 13.Is 100282 divisible by 19?
  14. 14.Is 18632 divisible by 24?
  15. 15.Is 26732 divisible by 4?
  16. 16.Is 132601 divisible by 19?
  17. 17.Is 27962 divisible by 11?
  18. 18.Is 87066 divisible by 30?
  19. 19.Is 42101 divisible by 7?
  20. 20.Is 15876 divisible by 3?
  21. 21.Is 32180 divisible by 5?
  22. 22.Is 7543 divisible by 19?
  23. 23.Is 3528 divisible by 12?
  24. 24.Is 31031 divisible by 23?
  25. 25.Is 42323 divisible by 7?
  26. 26.Is 13241 divisible by 2?
  27. 27.Is 9339 divisible by 3?
  28. 28.Is 34220 divisible by 29?
  29. 29.Is 47160 divisible by 30?
  30. 30.Is 57247 divisible by 19?
  31. 31.Is 56727 divisible by 9?
  32. 32.Is 24012 divisible by 18?
  33. 33.Is 15015 divisible by 7?
  34. 34.Is 21760 divisible by 4?
  35. 35.Is 45144 divisible by 23?
  36. 36.Is 81473 divisible by 13?
  37. 37.Is 125334 divisible by 18?
  38. 38.Is 38087 divisible by 6?
  39. 39.Is 70679 divisible by 23?
  40. 40.Is 39936 divisible by 24?

Answer key

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

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