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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 813 · 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 43162 divisible by 13?
  2. 2.Is 32087 divisible by 7?
  3. 3.Is 26505 divisible by 8?
  4. 4.Is 1032 divisible by 5?
  5. 5.Is 64316 divisible by 13?
  6. 6.Is 5225 divisible by 19?
  7. 7.Is 145153 divisible by 23?
  8. 8.Is 8618 divisible by 15?
  9. 9.Is 16041 divisible by 3?
  10. 10.Is 35070 divisible by 7?
  11. 11.Is 151235 divisible by 29?
  12. 12.Is 39940 divisible by 18?
  13. 13.Is 83896 divisible by 19?
  14. 14.Is 54723 divisible by 17?
  15. 15.Is 82654 divisible by 13?
  16. 16.Is 152337 divisible by 24?
  17. 17.Is 28512 divisible by 6?
  18. 18.Is 3525 divisible by 3?
  19. 19.Is 122196 divisible by 20?
  20. 20.Is 423 divisible by 3?
  21. 21.Is 31702 divisible by 19?
  22. 22.Is 11244 divisible by 6?
  23. 23.Is 27120 divisible by 30?
  24. 24.Is 2799 divisible by 8?
  25. 25.Is 85043 divisible by 18?
  26. 26.Is 7431 divisible by 3?
  27. 27.Is 110214 divisible by 18?
  28. 28.Is 16926 divisible by 13?
  29. 29.Is 686 divisible by 7?
  30. 30.Is 14530 divisible by 10?
  31. 31.Is 29482 divisible by 20?
  32. 32.Is 41677 divisible by 8?
  33. 33.Is 23725 divisible by 5?
  34. 34.Is 116493 divisible by 29?
  35. 35.Is 81383 divisible by 30?
  36. 36.Is 2967 divisible by 3?
  37. 37.Is 35166 divisible by 6?
  38. 38.Is 125640 divisible by 24?
  39. 39.Is 2824 divisible by 7?
  40. 40.Is 5905 divisible by 3?

Answer key

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

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