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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 945 · 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 4010 divisible by 6?
  2. 2.Is 114351 divisible by 20?
  3. 3.Is 18258 divisible by 7?
  4. 4.Is 26056 divisible by 4?
  5. 5.Is 45040 divisible by 24?
  6. 6.Is 14741 divisible by 11?
  7. 7.Is 34523 divisible by 23?
  8. 8.Is 7380 divisible by 4?
  9. 9.Is 49675 divisible by 20?
  10. 10.Is 4585 divisible by 2?
  11. 11.Is 14364 divisible by 7?
  12. 12.Is 43569 divisible by 10?
  13. 13.Is 34533 divisible by 9?
  14. 14.Is 55395 divisible by 9?
  15. 15.Is 105142 divisible by 30?
  16. 16.Is 81024 divisible by 24?
  17. 17.Is 41308 divisible by 29?
  18. 18.Is 20262 divisible by 6?
  19. 19.Is 164501 divisible by 30?
  20. 20.Is 189751 divisible by 30?
  21. 21.Is 122189 divisible by 19?
  22. 22.Is 73208 divisible by 13?
  23. 23.Is 3797 divisible by 23?
  24. 24.Is 60277 divisible by 24?
  25. 25.Is 159990 divisible by 30?
  26. 26.Is 25428 divisible by 13?
  27. 27.Is 33047 divisible by 7?
  28. 28.Is 50051 divisible by 13?
  29. 29.Is 52170 divisible by 15?
  30. 30.Is 88628 divisible by 15?
  31. 31.Is 30275 divisible by 5?
  32. 32.Is 20377 divisible by 17?
  33. 33.Is 101966 divisible by 17?
  34. 34.Is 24944 divisible by 4?
  35. 35.Is 68055 divisible by 15?
  36. 36.Is 6268 divisible by 2?
  37. 37.Is 44163 divisible by 7?
  38. 38.Is 4386 divisible by 17?
  39. 39.Is 22876 divisible by 30?
  40. 40.Is 2490 divisible by 3?

Answer key

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

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