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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 232 · 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 188065 divisible by 29?
  2. 2.Is 21648 divisible by 11?
  3. 3.Is 34719 divisible by 13?
  4. 4.Is 97940 divisible by 20?
  5. 5.Is 134711 divisible by 23?
  6. 6.Is 15809 divisible by 10?
  7. 7.Is 63550 divisible by 19?
  8. 8.Is 63348 divisible by 18?
  9. 9.Is 3067 divisible by 6?
  10. 10.Is 22583 divisible by 11?
  11. 11.Is 68816 divisible by 23?
  12. 12.Is 18797 divisible by 15?
  13. 13.Is 2997 divisible by 3?
  14. 14.Is 33876 divisible by 11?
  15. 15.Is 1098 divisible by 9?
  16. 16.Is 20790 divisible by 11?
  17. 17.Is 85363 divisible by 18?
  18. 18.Is 12351 divisible by 7?
  19. 19.Is 29169 divisible by 9?
  20. 20.Is 3737 divisible by 12?
  21. 21.Is 10036 divisible by 11?
  22. 22.Is 11913 divisible by 2?
  23. 23.Is 11578 divisible by 3?
  24. 24.Is 157632 divisible by 24?
  25. 25.Is 80460 divisible by 12?
  26. 26.Is 64958 divisible by 10?
  27. 27.Is 7038 divisible by 13?
  28. 28.Is 18768 divisible by 12?
  29. 29.Is 46709 divisible by 13?
  30. 30.Is 38371 divisible by 23?
  31. 31.Is 65773 divisible by 19?
  32. 32.Is 59460 divisible by 30?
  33. 33.Is 11358 divisible by 2?
  34. 34.Is 25786 divisible by 11?
  35. 35.Is 7361 divisible by 5?
  36. 36.Is 3316 divisible by 9?
  37. 37.Is 165404 divisible by 24?
  38. 38.Is 7994 divisible by 7?
  39. 39.Is 13748 divisible by 3?
  40. 40.Is 10944 divisible by 4?

Answer key

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

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