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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 305 · 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 172966 divisible by 29?
  2. 2.Is 55699 divisible by 13?
  3. 3.Is 194649 divisible by 29?
  4. 4.Is 55995 divisible by 15?
  5. 5.Is 37757 divisible by 9?
  6. 6.Is 19275 divisible by 18?
  7. 7.Is 25623 divisible by 6?
  8. 8.Is 5353 divisible by 2?
  9. 9.Is 20709 divisible by 9?
  10. 10.Is 110827 divisible by 19?
  11. 11.Is 41534 divisible by 7?
  12. 12.Is 39390 divisible by 10?
  13. 13.Is 37280 divisible by 11?
  14. 14.Is 93798 divisible by 18?
  15. 15.Is 3826 divisible by 8?
  16. 16.Is 14193 divisible by 30?
  17. 17.Is 64003 divisible by 12?
  18. 18.Is 23721 divisible by 10?
  19. 19.Is 2303 divisible by 2?
  20. 20.Is 50420 divisible by 20?
  21. 21.Is 44411 divisible by 10?
  22. 22.Is 94643 divisible by 19?
  23. 23.Is 16002 divisible by 18?
  24. 24.Is 104123 divisible by 29?
  25. 25.Is 444 divisible by 6?
  26. 26.Is 114724 divisible by 29?
  27. 27.Is 151704 divisible by 24?
  28. 28.Is 6953 divisible by 2?
  29. 29.Is 124296 divisible by 24?
  30. 30.Is 38894 divisible by 13?
  31. 31.Is 3642 divisible by 3?
  32. 32.Is 61860 divisible by 20?
  33. 33.Is 62472 divisible by 24?
  34. 34.Is 37191 divisible by 23?
  35. 35.Is 63275 divisible by 23?
  36. 36.Is 158856 divisible by 24?
  37. 37.Is 47816 divisible by 8?
  38. 38.Is 2839 divisible by 17?
  39. 39.Is 15560 divisible by 5?
  40. 40.Is 28225 divisible by 23?

Answer key

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

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