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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 792 · 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 35167 divisible by 23?
  2. 2.Is 30257 divisible by 30?
  3. 3.Is 15574 divisible by 3?
  4. 4.Is 37689 divisible by 9?
  5. 5.Is 41314 divisible by 13?
  6. 6.Is 20620 divisible by 20?
  7. 7.Is 69094 divisible by 12?
  8. 8.Is 9680 divisible by 8?
  9. 9.Is 34230 divisible by 5?
  10. 10.Is 70350 divisible by 30?
  11. 11.Is 18931 divisible by 5?
  12. 12.Is 54810 divisible by 18?
  13. 13.Is 3750 divisible by 10?
  14. 14.Is 1260 divisible by 2?
  15. 15.Is 5146 divisible by 2?
  16. 16.Is 40391 divisible by 8?
  17. 17.Is 44388 divisible by 7?
  18. 18.Is 26831 divisible by 7?
  19. 19.Is 20146 divisible by 3?
  20. 20.Is 31635 divisible by 19?
  21. 21.Is 33534 divisible by 5?
  22. 22.Is 62704 divisible by 13?
  23. 23.Is 26278 divisible by 7?
  24. 24.Is 123188 divisible by 23?
  25. 25.Is 3159 divisible by 13?
  26. 26.Is 56678 divisible by 17?
  27. 27.Is 93668 divisible by 20?
  28. 28.Is 7820 divisible by 3?
  29. 29.Is 59610 divisible by 15?
  30. 30.Is 2380 divisible by 4?
  31. 31.Is 10900 divisible by 4?
  32. 32.Is 61452 divisible by 9?
  33. 33.Is 126827 divisible by 29?
  34. 34.Is 25751 divisible by 11?
  35. 35.Is 69230 divisible by 13?
  36. 36.Is 43533 divisible by 7?
  37. 37.Is 51970 divisible by 10?
  38. 38.Is 69905 divisible by 12?
  39. 39.Is 26672 divisible by 4?
  40. 40.Is 44921 divisible by 9?

Answer key

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

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