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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 931 · 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 9195 divisible by 5?
  2. 2.Is 24384 divisible by 17?
  3. 3.Is 140592 divisible by 29?
  4. 4.Is 50653 divisible by 11?
  5. 5.Is 41721 divisible by 13?
  6. 6.Is 9251 divisible by 7?
  7. 7.Is 29322 divisible by 20?
  8. 8.Is 79165 divisible by 20?
  9. 9.Is 43080 divisible by 10?
  10. 10.Is 134133 divisible by 29?
  11. 11.Is 25237 divisible by 9?
  12. 12.Is 97376 divisible by 17?
  13. 13.Is 4113 divisible by 3?
  14. 14.Is 94487 divisible by 19?
  15. 15.Is 20737 divisible by 8?
  16. 16.Is 132821 divisible by 29?
  17. 17.Is 134920 divisible by 20?
  18. 18.Is 57540 divisible by 30?
  19. 19.Is 105454 divisible by 30?
  20. 20.Is 35283 divisible by 9?
  21. 21.Is 4009 divisible by 5?
  22. 22.Is 40839 divisible by 17?
  23. 23.Is 7043 divisible by 7?
  24. 24.Is 10868 divisible by 11?
  25. 25.Is 7360 divisible by 20?
  26. 26.Is 89777 divisible by 17?
  27. 27.Is 4764 divisible by 3?
  28. 28.Is 5551 divisible by 4?
  29. 29.Is 82776 divisible by 19?
  30. 30.Is 79625 divisible by 13?
  31. 31.Is 88961 divisible by 17?
  32. 32.Is 65884 divisible by 23?
  33. 33.Is 87783 divisible by 29?
  34. 34.Is 14960 divisible by 12?
  35. 35.Is 38934 divisible by 13?
  36. 36.Is 181938 divisible by 30?
  37. 37.Is 139007 divisible by 29?
  38. 38.Is 23207 divisible by 6?
  39. 39.Is 10948 divisible by 13?
  40. 40.Is 25186 divisible by 12?

Answer key

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

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