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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 272 · 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 50835 divisible by 15?
  2. 2.Is 26538 divisible by 11?
  3. 3.Is 11012 divisible by 4?
  4. 4.Is 70323 divisible by 17?
  5. 5.Is 9324 divisible by 7?
  6. 6.Is 80449 divisible by 18?
  7. 7.Is 116982 divisible by 18?
  8. 8.Is 11960 divisible by 10?
  9. 9.Is 157194 divisible by 24?
  10. 10.Is 25741 divisible by 15?
  11. 11.Is 18792 divisible by 3?
  12. 12.Is 34356 divisible by 12?
  13. 13.Is 17505 divisible by 4?
  14. 14.Is 33341 divisible by 7?
  15. 15.Is 4144 divisible by 8?
  16. 16.Is 9961 divisible by 20?
  17. 17.Is 10916 divisible by 2?
  18. 18.Is 4608 divisible by 17?
  19. 19.Is 66668 divisible by 12?
  20. 20.Is 18705 divisible by 5?
  21. 21.Is 27600 divisible by 18?
  22. 22.Is 2374 divisible by 2?
  23. 23.Is 33732 divisible by 5?
  24. 24.Is 26314 divisible by 7?
  25. 25.Is 1528 divisible by 3?
  26. 26.Is 26238 divisible by 8?
  27. 27.Is 29013 divisible by 6?
  28. 28.Is 39529 divisible by 11?
  29. 29.Is 2802 divisible by 6?
  30. 30.Is 188385 divisible by 29?
  31. 31.Is 16903 divisible by 12?
  32. 32.Is 134770 divisible by 24?
  33. 33.Is 66090 divisible by 30?
  34. 34.Is 12438 divisible by 6?
  35. 35.Is 1885 divisible by 29?
  36. 36.Is 5520 divisible by 15?
  37. 37.Is 100249 divisible by 15?
  38. 38.Is 20085 divisible by 6?
  39. 39.Is 148373 divisible by 23?
  40. 40.Is 80832 divisible by 24?

Answer key

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

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