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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 428 · 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 19123 divisible by 3?
  2. 2.Is 28634 divisible by 12?
  3. 3.Is 90120 divisible by 24?
  4. 4.Is 11296 divisible by 3?
  5. 5.Is 27048 divisible by 24?
  6. 6.Is 76200 divisible by 30?
  7. 7.Is 18423 divisible by 23?
  8. 8.Is 40696 divisible by 8?
  9. 9.Is 107802 divisible by 18?
  10. 10.Is 18271 divisible by 5?
  11. 11.Is 14267 divisible by 17?
  12. 12.Is 87803 divisible by 20?
  13. 13.Is 10817 divisible by 4?
  14. 14.Is 3240 divisible by 2?
  15. 15.Is 27042 divisible by 13?
  16. 16.Is 35777 divisible by 17?
  17. 17.Is 9647 divisible by 17?
  18. 18.Is 29818 divisible by 6?
  19. 19.Is 51819 divisible by 9?
  20. 20.Is 47593 divisible by 7?
  21. 21.Is 55200 divisible by 24?
  22. 22.Is 33959 divisible by 29?
  23. 23.Is 82727 divisible by 15?
  24. 24.Is 25943 divisible by 12?
  25. 25.Is 958 divisible by 2?
  26. 26.Is 43752 divisible by 7?
  27. 27.Is 15108 divisible by 6?
  28. 28.Is 32849 divisible by 24?
  29. 29.Is 6909 divisible by 9?
  30. 30.Is 26404 divisible by 7?
  31. 31.Is 39232 divisible by 8?
  32. 32.Is 62560 divisible by 20?
  33. 33.Is 127224 divisible by 24?
  34. 34.Is 68910 divisible by 30?
  35. 35.Is 105453 divisible by 20?
  36. 36.Is 24171 divisible by 9?
  37. 37.Is 8874 divisible by 3?
  38. 38.Is 30085 divisible by 8?
  39. 39.Is 26801 divisible by 15?
  40. 40.Is 41478 divisible by 11?

Answer key

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

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