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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 470 · 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 5761 divisible by 20?
  2. 2.Is 1375 divisible by 2?
  3. 3.Is 145244 divisible by 30?
  4. 4.Is 23660 divisible by 4?
  5. 5.Is 58300 divisible by 20?
  6. 6.Is 4528 divisible by 3?
  7. 7.Is 9438 divisible by 13?
  8. 8.Is 45859 divisible by 11?
  9. 9.Is 73525 divisible by 23?
  10. 10.Is 104386 divisible by 19?
  11. 11.Is 62322 divisible by 11?
  12. 12.Is 5698 divisible by 3?
  13. 13.Is 138128 divisible by 30?
  14. 14.Is 48348 divisible by 12?
  15. 15.Is 49185 divisible by 17?
  16. 16.Is 85065 divisible by 15?
  17. 17.Is 6501 divisible by 11?
  18. 18.Is 584 divisible by 8?
  19. 19.Is 39258 divisible by 8?
  20. 20.Is 66735 divisible by 15?
  21. 21.Is 9423 divisible by 3?
  22. 22.Is 7296 divisible by 5?
  23. 23.Is 73265 divisible by 30?
  24. 24.Is 34850 divisible by 5?
  25. 25.Is 2736 divisible by 15?
  26. 26.Is 112138 divisible by 23?
  27. 27.Is 31806 divisible by 18?
  28. 28.Is 14792 divisible by 4?
  29. 29.Is 11565 divisible by 2?
  30. 30.Is 22424 divisible by 8?
  31. 31.Is 2382 divisible by 3?
  32. 32.Is 13530 divisible by 11?
  33. 33.Is 94753 divisible by 19?
  34. 34.Is 1791 divisible by 5?
  35. 35.Is 7429 divisible by 6?
  36. 36.Is 6426 divisible by 3?
  37. 37.Is 3829 divisible by 7?
  38. 38.Is 24248 divisible by 7?
  39. 39.Is 45689 divisible by 7?
  40. 40.Is 113640 divisible by 24?

Answer key

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

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