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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 589 · 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 7956 divisible by 6?
  2. 2.Is 39207 divisible by 23?
  3. 3.Is 65964 divisible by 23?
  4. 4.Is 35490 divisible by 13?
  5. 5.Is 122112 divisible by 24?
  6. 6.Is 6079 divisible by 3?
  7. 7.Is 44301 divisible by 15?
  8. 8.Is 53613 divisible by 9?
  9. 9.Is 22940 divisible by 7?
  10. 10.Is 85632 divisible by 15?
  11. 11.Is 22024 divisible by 4?
  12. 12.Is 69890 divisible by 12?
  13. 13.Is 24904 divisible by 7?
  14. 14.Is 27555 divisible by 15?
  15. 15.Is 92456 divisible by 23?
  16. 16.Is 15434 divisible by 5?
  17. 17.Is 9894 divisible by 3?
  18. 18.Is 189888 divisible by 29?
  19. 19.Is 20908 divisible by 6?
  20. 20.Is 40397 divisible by 9?
  21. 21.Is 109884 divisible by 29?
  22. 22.Is 26564 divisible by 10?
  23. 23.Is 133837 divisible by 23?
  24. 24.Is 10680 divisible by 2?
  25. 25.Is 38070 divisible by 10?
  26. 26.Is 63568 divisible by 29?
  27. 27.Is 95098 divisible by 17?
  28. 28.Is 28133 divisible by 6?
  29. 29.Is 190440 divisible by 30?
  30. 30.Is 20340 divisible by 3?
  31. 31.Is 48618 divisible by 9?
  32. 32.Is 17757 divisible by 3?
  33. 33.Is 104498 divisible by 29?
  34. 34.Is 43470 divisible by 9?
  35. 35.Is 10307 divisible by 3?
  36. 36.Is 42610 divisible by 19?
  37. 37.Is 2798 divisible by 2?
  38. 38.Is 98234 divisible by 30?
  39. 39.Is 117082 divisible by 30?
  40. 40.Is 16597 divisible by 13?

Answer key

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

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