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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 676 · 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 22806 divisible by 11?
  2. 2.Is 46959 divisible by 8?
  3. 3.Is 2605 divisible by 12?
  4. 4.Is 7873 divisible by 5?
  5. 5.Is 22057 divisible by 4?
  6. 6.Is 1536 divisible by 3?
  7. 7.Is 99840 divisible by 20?
  8. 8.Is 17885 divisible by 5?
  9. 9.Is 74500 divisible by 20?
  10. 10.Is 40992 divisible by 7?
  11. 11.Is 4286 divisible by 5?
  12. 12.Is 47893 divisible by 9?
  13. 13.Is 84749 divisible by 13?
  14. 14.Is 93521 divisible by 30?
  15. 15.Is 31272 divisible by 24?
  16. 16.Is 43830 divisible by 9?
  17. 17.Is 6895 divisible by 5?
  18. 18.Is 77400 divisible by 12?
  19. 19.Is 2328 divisible by 12?
  20. 20.Is 61468 divisible by 11?
  21. 21.Is 8531 divisible by 19?
  22. 22.Is 24668 divisible by 10?
  23. 23.Is 2008 divisible by 11?
  24. 24.Is 18234 divisible by 6?
  25. 25.Is 27555 divisible by 15?
  26. 26.Is 47268 divisible by 9?
  27. 27.Is 20520 divisible by 12?
  28. 28.Is 29841 divisible by 10?
  29. 29.Is 13648 divisible by 4?
  30. 30.Is 2830 divisible by 2?
  31. 31.Is 89433 divisible by 17?
  32. 32.Is 7309 divisible by 2?
  33. 33.Is 61692 divisible by 11?
  34. 34.Is 4372 divisible by 8?
  35. 35.Is 148281 divisible by 23?
  36. 36.Is 46057 divisible by 7?
  37. 37.Is 3095 divisible by 10?
  38. 38.Is 36278 divisible by 11?
  39. 39.Is 29970 divisible by 5?
  40. 40.Is 26214 divisible by 17?

Answer key

  1. no
  2. no
  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. yes
  17. yes
  18. yes
  19. yes
  20. yes
  21. yes
  22. no
  23. no
  24. yes
  25. yes
  26. yes
  27. yes
  28. no
  29. yes
  30. yes
  31. no
  32. no
  33. no
  34. no
  35. yes
  36. no
  37. no
  38. yes
  39. yes
  40. yes

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