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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 752 · 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 123523 divisible by 23?
  2. 2.Is 11819 divisible by 2?
  3. 3.Is 1914 divisible by 4?
  4. 4.Is 24711 divisible by 10?
  5. 5.Is 6457 divisible by 3?
  6. 6.Is 497 divisible by 9?
  7. 7.Is 92463 divisible by 15?
  8. 8.Is 26938 divisible by 15?
  9. 9.Is 42426 divisible by 18?
  10. 10.Is 51793 divisible by 11?
  11. 11.Is 99231 divisible by 30?
  12. 12.Is 2970 divisible by 5?
  13. 13.Is 78509 divisible by 19?
  14. 14.Is 103890 divisible by 15?
  15. 15.Is 13696 divisible by 24?
  16. 16.Is 80430 divisible by 15?
  17. 17.Is 20197 divisible by 10?
  18. 18.Is 65713 divisible by 19?
  19. 19.Is 20296 divisible by 8?
  20. 20.Is 38623 divisible by 13?
  21. 21.Is 68719 divisible by 12?
  22. 22.Is 33272 divisible by 8?
  23. 23.Is 68953 divisible by 10?
  24. 24.Is 86815 divisible by 13?
  25. 25.Is 27270 divisible by 15?
  26. 26.Is 10475 divisible by 5?
  27. 27.Is 34232 divisible by 8?
  28. 28.Is 6582 divisible by 4?
  29. 29.Is 15008 divisible by 7?
  30. 30.Is 2996 divisible by 7?
  31. 31.Is 6528 divisible by 5?
  32. 32.Is 9534 divisible by 7?
  33. 33.Is 14313 divisible by 3?
  34. 34.Is 16939 divisible by 4?
  35. 35.Is 167301 divisible by 29?
  36. 36.Is 157590 divisible by 23?
  37. 37.Is 70763 divisible by 15?
  38. 38.Is 8057 divisible by 7?
  39. 39.Is 23692 divisible by 7?
  40. 40.Is 14922 divisible by 18?

Answer key

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

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