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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 655 · 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 6227 divisible by 13?
  2. 2.Is 183600 divisible by 30?
  3. 3.Is 4194 divisible by 3?
  4. 4.Is 132820 divisible by 29?
  5. 5.Is 22880 divisible by 8?
  6. 6.Is 22352 divisible by 12?
  7. 7.Is 29540 divisible by 9?
  8. 8.Is 27675 divisible by 10?
  9. 9.Is 17765 divisible by 10?
  10. 10.Is 38076 divisible by 6?
  11. 11.Is 16620 divisible by 13?
  12. 12.Is 122173 divisible by 23?
  13. 13.Is 5152 divisible by 2?
  14. 14.Is 10120 divisible by 9?
  15. 15.Is 69048 divisible by 24?
  16. 16.Is 12624 divisible by 24?
  17. 17.Is 11405 divisible by 2?
  18. 18.Is 15476 divisible by 4?
  19. 19.Is 137469 divisible by 23?
  20. 20.Is 13068 divisible by 9?
  21. 21.Is 19708 divisible by 11?
  22. 22.Is 28455 divisible by 15?
  23. 23.Is 9149 divisible by 30?
  24. 24.Is 10146 divisible by 2?
  25. 25.Is 20977 divisible by 11?
  26. 26.Is 125296 divisible by 20?
  27. 27.Is 8886 divisible by 2?
  28. 28.Is 14844 divisible by 3?
  29. 29.Is 27835 divisible by 4?
  30. 30.Is 14476 divisible by 13?
  31. 31.Is 52353 divisible by 9?
  32. 32.Is 3007 divisible by 7?
  33. 33.Is 37557 divisible by 6?
  34. 34.Is 8178 divisible by 3?
  35. 35.Is 35412 divisible by 12?
  36. 36.Is 15504 divisible by 17?
  37. 37.Is 18457 divisible by 5?
  38. 38.Is 19721 divisible by 23?
  39. 39.Is 46377 divisible by 13?
  40. 40.Is 12523 divisible by 23?

Answer key

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

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