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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 362 · 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 3479 divisible by 7?
  2. 2.Is 7485 divisible by 4?
  3. 3.Is 110500 divisible by 19?
  4. 4.Is 12412 divisible by 17?
  5. 5.Is 2411 divisible by 6?
  6. 6.Is 9404 divisible by 9?
  7. 7.Is 39440 divisible by 6?
  8. 8.Is 71193 divisible by 19?
  9. 9.Is 43641 divisible by 13?
  10. 10.Is 58020 divisible by 15?
  11. 11.Is 10109 divisible by 4?
  12. 12.Is 11669 divisible by 4?
  13. 13.Is 4929 divisible by 4?
  14. 14.Is 113145 divisible by 19?
  15. 15.Is 17095 divisible by 13?
  16. 16.Is 130065 divisible by 29?
  17. 17.Is 123186 divisible by 23?
  18. 18.Is 58531 divisible by 17?
  19. 19.Is 101858 divisible by 17?
  20. 20.Is 13912 divisible by 6?
  21. 21.Is 78804 divisible by 19?
  22. 22.Is 24574 divisible by 5?
  23. 23.Is 66690 divisible by 15?
  24. 24.Is 52441 divisible by 9?
  25. 25.Is 4399 divisible by 6?
  26. 26.Is 24180 divisible by 6?
  27. 27.Is 58298 divisible by 10?
  28. 28.Is 65016 divisible by 12?
  29. 29.Is 140856 divisible by 24?
  30. 30.Is 230 divisible by 6?
  31. 31.Is 99210 divisible by 30?
  32. 32.Is 3144 divisible by 6?
  33. 33.Is 5646 divisible by 9?
  34. 34.Is 159958 divisible by 30?
  35. 35.Is 22554 divisible by 6?
  36. 36.Is 1433 divisible by 2?
  37. 37.Is 36792 divisible by 7?
  38. 38.Is 19588 divisible by 10?
  39. 39.Is 7898 divisible by 10?
  40. 40.Is 4244 divisible by 7?

Answer key

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

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