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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 563 · 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 90390 divisible by 23?
  2. 2.Is 107617 divisible by 23?
  3. 3.Is 10028 divisible by 2?
  4. 4.Is 8239 divisible by 11?
  5. 5.Is 30774 divisible by 5?
  6. 6.Is 25302 divisible by 6?
  7. 7.Is 12369 divisible by 6?
  8. 8.Is 224 divisible by 5?
  9. 9.Is 10100 divisible by 2?
  10. 10.Is 994 divisible by 7?
  11. 11.Is 202083 divisible by 30?
  12. 12.Is 19611 divisible by 3?
  13. 13.Is 133292 divisible by 29?
  14. 14.Is 17785 divisible by 5?
  15. 15.Is 54279 divisible by 13?
  16. 16.Is 10025 divisible by 2?
  17. 17.Is 10423 divisible by 10?
  18. 18.Is 34460 divisible by 17?
  19. 19.Is 30221 divisible by 29?
  20. 20.Is 75318 divisible by 11?
  21. 21.Is 28329 divisible by 7?
  22. 22.Is 66671 divisible by 19?
  23. 23.Is 106760 divisible by 20?
  24. 24.Is 18456 divisible by 8?
  25. 25.Is 13552 divisible by 11?
  26. 26.Is 32725 divisible by 7?
  27. 27.Is 3173 divisible by 2?
  28. 28.Is 11442 divisible by 2?
  29. 29.Is 25890 divisible by 30?
  30. 30.Is 25052 divisible by 29?
  31. 31.Is 11904 divisible by 17?
  32. 32.Is 30202 divisible by 18?
  33. 33.Is 32601 divisible by 5?
  34. 34.Is 840 divisible by 6?
  35. 35.Is 201666 divisible by 29?
  36. 36.Is 31705 divisible by 5?
  37. 37.Is 13000 divisible by 5?
  38. 38.Is 66450 divisible by 15?
  39. 39.Is 44011 divisible by 7?
  40. 40.Is 20416 divisible by 4?

Answer key

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

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