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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 533 · 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 74041 divisible by 17?
  2. 2.Is 40256 divisible by 7?
  3. 3.Is 5884 divisible by 2?
  4. 4.Is 42313 divisible by 12?
  5. 5.Is 40896 divisible by 18?
  6. 6.Is 59169 divisible by 10?
  7. 7.Is 120408 divisible by 29?
  8. 8.Is 14370 divisible by 9?
  9. 9.Is 96071 divisible by 23?
  10. 10.Is 20322 divisible by 3?
  11. 11.Is 61248 divisible by 29?
  12. 12.Is 110310 divisible by 30?
  13. 13.Is 4093 divisible by 2?
  14. 14.Is 84483 divisible by 23?
  15. 15.Is 13800 divisible by 24?
  16. 16.Is 48159 divisible by 8?
  17. 17.Is 2820 divisible by 4?
  18. 18.Is 48006 divisible by 7?
  19. 19.Is 21450 divisible by 11?
  20. 20.Is 104565 divisible by 15?
  21. 21.Is 32223 divisible by 18?
  22. 22.Is 27482 divisible by 29?
  23. 23.Is 66658 divisible by 18?
  24. 24.Is 50935 divisible by 18?
  25. 25.Is 2276 divisible by 3?
  26. 26.Is 78375 divisible by 15?
  27. 27.Is 8651 divisible by 6?
  28. 28.Is 5586 divisible by 19?
  29. 29.Is 22162 divisible by 6?
  30. 30.Is 106965 divisible by 17?
  31. 31.Is 112060 divisible by 18?
  32. 32.Is 16332 divisible by 4?
  33. 33.Is 4584 divisible by 10?
  34. 34.Is 3295 divisible by 5?
  35. 35.Is 103412 divisible by 18?
  36. 36.Is 62180 divisible by 15?
  37. 37.Is 7824 divisible by 24?
  38. 38.Is 53940 divisible by 30?
  39. 39.Is 52872 divisible by 8?
  40. 40.Is 56086 divisible by 29?

Answer key

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

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