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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 49 · 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 52619 divisible by 10?
  2. 2.Is 70608 divisible by 29?
  3. 3.Is 42834 divisible by 10?
  4. 4.Is 2505 divisible by 3?
  5. 5.Is 17863 divisible by 12?
  6. 6.Is 5160 divisible by 11?
  7. 7.Is 99545 divisible by 17?
  8. 8.Is 3616 divisible by 6?
  9. 9.Is 45638 divisible by 7?
  10. 10.Is 19941 divisible by 23?
  11. 11.Is 105547 divisible by 23?
  12. 12.Is 22800 divisible by 24?
  13. 13.Is 61932 divisible by 18?
  14. 14.Is 11249 divisible by 2?
  15. 15.Is 58522 divisible by 29?
  16. 16.Is 13149 divisible by 3?
  17. 17.Is 8906 divisible by 20?
  18. 18.Is 1760 divisible by 10?
  19. 19.Is 16676 divisible by 19?
  20. 20.Is 4084 divisible by 4?
  21. 21.Is 2766 divisible by 2?
  22. 22.Is 12165 divisible by 3?
  23. 23.Is 3136 divisible by 4?
  24. 24.Is 10112 divisible by 2?
  25. 25.Is 159020 divisible by 23?
  26. 26.Is 90226 divisible by 20?
  27. 27.Is 31585 divisible by 6?
  28. 28.Is 84625 divisible by 20?
  29. 29.Is 24514 divisible by 7?
  30. 30.Is 15526 divisible by 7?
  31. 31.Is 46287 divisible by 10?
  32. 32.Is 55534 divisible by 13?
  33. 33.Is 7882 divisible by 7?
  34. 34.Is 148465 divisible by 23?
  35. 35.Is 81011 divisible by 13?
  36. 36.Is 72289 divisible by 23?
  37. 37.Is 28056 divisible by 5?
  38. 38.Is 63138 divisible by 24?
  39. 39.Is 42138 divisible by 11?
  40. 40.Is 142506 divisible by 29?

Answer key

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

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