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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 385 · 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 81635 divisible by 29?
  2. 2.Is 70602 divisible by 19?
  3. 3.Is 44980 divisible by 8?
  4. 4.Is 48164 divisible by 17?
  5. 5.Is 4941 divisible by 2?
  6. 6.Is 56568 divisible by 29?
  7. 7.Is 59350 divisible by 29?
  8. 8.Is 13337 divisible by 15?
  9. 9.Is 10498 divisible by 2?
  10. 10.Is 15708 divisible by 3?
  11. 11.Is 9963 divisible by 9?
  12. 12.Is 31641 divisible by 19?
  13. 13.Is 20360 divisible by 20?
  14. 14.Is 3829 divisible by 3?
  15. 15.Is 49580 divisible by 9?
  16. 16.Is 25648 divisible by 8?
  17. 17.Is 35560 divisible by 7?
  18. 18.Is 113434 divisible by 17?
  19. 19.Is 9639 divisible by 13?
  20. 20.Is 6357 divisible by 11?
  21. 21.Is 1121 divisible by 2?
  22. 22.Is 40070 divisible by 10?
  23. 23.Is 3565 divisible by 23?
  24. 24.Is 45734 divisible by 29?
  25. 25.Is 5670 divisible by 3?
  26. 26.Is 52450 divisible by 10?
  27. 27.Is 52719 divisible by 13?
  28. 28.Is 31570 divisible by 5?
  29. 29.Is 63292 divisible by 10?
  30. 30.Is 9795 divisible by 30?
  31. 31.Is 41969 divisible by 8?
  32. 32.Is 89917 divisible by 29?
  33. 33.Is 23060 divisible by 9?
  34. 34.Is 16468 divisible by 23?
  35. 35.Is 69300 divisible by 10?
  36. 36.Is 7425 divisible by 15?
  37. 37.Is 75797 divisible by 11?
  38. 38.Is 204706 divisible by 30?
  39. 39.Is 110785 divisible by 30?
  40. 40.Is 4890 divisible by 6?

Answer key

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

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