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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 925 · 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 26022 divisible by 23?
  2. 2.Is 35509 divisible by 12?
  3. 3.Is 7681 divisible by 29?
  4. 4.Is 34380 divisible by 18?
  5. 5.Is 104910 divisible by 15?
  6. 6.Is 194850 divisible by 30?
  7. 7.Is 51600 divisible by 15?
  8. 8.Is 7800 divisible by 10?
  9. 9.Is 58649 divisible by 13?
  10. 10.Is 27214 divisible by 19?
  11. 11.Is 44425 divisible by 8?
  12. 12.Is 43888 divisible by 13?
  13. 13.Is 65511 divisible by 29?
  14. 14.Is 53157 divisible by 29?
  15. 15.Is 7888 divisible by 8?
  16. 16.Is 59114 divisible by 11?
  17. 17.Is 10326 divisible by 23?
  18. 18.Is 8456 divisible by 2?
  19. 19.Is 151 divisible by 7?
  20. 20.Is 104600 divisible by 15?
  21. 21.Is 71876 divisible by 17?
  22. 22.Is 5966 divisible by 4?
  23. 23.Is 15828 divisible by 5?
  24. 24.Is 132216 divisible by 20?
  25. 25.Is 67995 divisible by 15?
  26. 26.Is 5344 divisible by 8?
  27. 27.Is 27520 divisible by 10?
  28. 28.Is 78259 divisible by 13?
  29. 29.Is 100326 divisible by 23?
  30. 30.Is 60994 divisible by 18?
  31. 31.Is 90701 divisible by 13?
  32. 32.Is 20486 divisible by 9?
  33. 33.Is 102551 divisible by 17?
  34. 34.Is 14508 divisible by 18?
  35. 35.Is 55090 divisible by 9?
  36. 36.Is 20770 divisible by 9?
  37. 37.Is 31760 divisible by 20?
  38. 38.Is 39910 divisible by 10?
  39. 39.Is 61464 divisible by 12?
  40. 40.Is 97376 divisible by 17?

Answer key

  1. no
  2. no
  3. no
  4. yes
  5. yes
  6. yes
  7. yes
  8. yes
  9. no
  10. no
  11. no
  12. yes
  13. yes
  14. yes
  15. yes
  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. no
  34. yes
  35. no
  36. no
  37. yes
  38. yes
  39. yes
  40. yes

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