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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 549 · 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 99541 divisible by 30?
  2. 2.Is 60028 divisible by 18?
  3. 3.Is 12990 divisible by 7?
  4. 4.Is 1073 divisible by 2?
  5. 5.Is 1305 divisible by 3?
  6. 6.Is 8471 divisible by 3?
  7. 7.Is 84615 divisible by 24?
  8. 8.Is 1026 divisible by 6?
  9. 9.Is 5906 divisible by 10?
  10. 10.Is 127 divisible by 2?
  11. 11.Is 8472 divisible by 8?
  12. 12.Is 10745 divisible by 5?
  13. 13.Is 53329 divisible by 9?
  14. 14.Is 31606 divisible by 6?
  15. 15.Is 5849 divisible by 6?
  16. 16.Is 7000 divisible by 10?
  17. 17.Is 45519 divisible by 11?
  18. 18.Is 119352 divisible by 24?
  19. 19.Is 30194 divisible by 11?
  20. 20.Is 17189 divisible by 4?
  21. 21.Is 28085 divisible by 5?
  22. 22.Is 45939 divisible by 12?
  23. 23.Is 40848 divisible by 6?
  24. 24.Is 49512 divisible by 10?
  25. 25.Is 7417 divisible by 7?
  26. 26.Is 35447 divisible by 10?
  27. 27.Is 14400 divisible by 6?
  28. 28.Is 138727 divisible by 20?
  29. 29.Is 68207 divisible by 11?
  30. 30.Is 36541 divisible by 11?
  31. 31.Is 37742 divisible by 10?
  32. 32.Is 106448 divisible by 30?
  33. 33.Is 19576 divisible by 5?
  34. 34.Is 63555 divisible by 15?
  35. 35.Is 122420 divisible by 20?
  36. 36.Is 88805 divisible by 13?
  37. 37.Is 98741 divisible by 18?
  38. 38.Is 25375 divisible by 4?
  39. 39.Is 105260 divisible by 20?
  40. 40.Is 132805 divisible by 23?

Answer key

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

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