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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 98 · 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 189900 divisible by 29?
  2. 2.Is 8700 divisible by 29?
  3. 3.Is 115020 divisible by 20?
  4. 4.Is 4429 divisible by 3?
  5. 5.Is 26525 divisible by 5?
  6. 6.Is 103839 divisible by 20?
  7. 7.Is 16812 divisible by 3?
  8. 8.Is 26917 divisible by 13?
  9. 9.Is 361 divisible by 3?
  10. 10.Is 26310 divisible by 9?
  11. 11.Is 25981 divisible by 8?
  12. 12.Is 50144 divisible by 15?
  13. 13.Is 5481 divisible by 29?
  14. 14.Is 33096 divisible by 24?
  15. 15.Is 64460 divisible by 13?
  16. 16.Is 47030 divisible by 11?
  17. 17.Is 45816 divisible by 24?
  18. 18.Is 15162 divisible by 19?
  19. 19.Is 131545 divisible by 19?
  20. 20.Is 24957 divisible by 9?
  21. 21.Is 963 divisible by 5?
  22. 22.Is 1473 divisible by 2?
  23. 23.Is 32192 divisible by 8?
  24. 24.Is 46422 divisible by 18?
  25. 25.Is 41616 divisible by 9?
  26. 26.Is 7662 divisible by 6?
  27. 27.Is 9250 divisible by 2?
  28. 28.Is 67311 divisible by 17?
  29. 29.Is 65804 divisible by 13?
  30. 30.Is 108395 divisible by 19?
  31. 31.Is 62389 divisible by 24?
  32. 32.Is 41626 divisible by 13?
  33. 33.Is 4805 divisible by 6?
  34. 34.Is 64598 divisible by 11?
  35. 35.Is 11837 divisible by 2?
  36. 36.Is 79835 divisible by 15?
  37. 37.Is 9975 divisible by 8?
  38. 38.Is 37138 divisible by 29?
  39. 39.Is 62413 divisible by 13?
  40. 40.Is 4769 divisible by 19?

Answer key

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

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