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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 953 · 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 36233 divisible by 7?
  2. 2.Is 34653 divisible by 17?
  3. 3.Is 69048 divisible by 12?
  4. 4.Is 1896 divisible by 8?
  5. 5.Is 57846 divisible by 18?
  6. 6.Is 22167 divisible by 9?
  7. 7.Is 5991 divisible by 9?
  8. 8.Is 2141 divisible by 7?
  9. 9.Is 12240 divisible by 5?
  10. 10.Is 90735 divisible by 23?
  11. 11.Is 104995 divisible by 23?
  12. 12.Is 32901 divisible by 11?
  13. 13.Is 101326 divisible by 15?
  14. 14.Is 11011 divisible by 3?
  15. 15.Is 5993 divisible by 7?
  16. 16.Is 84114 divisible by 19?
  17. 17.Is 70157 divisible by 18?
  18. 18.Is 1907 divisible by 2?
  19. 19.Is 53901 divisible by 10?
  20. 20.Is 97802 divisible by 20?
  21. 21.Is 14157 divisible by 13?
  22. 22.Is 31190 divisible by 10?
  23. 23.Is 1631 divisible by 7?
  24. 24.Is 74861 divisible by 23?
  25. 25.Is 5238 divisible by 9?
  26. 26.Is 57171 divisible by 19?
  27. 27.Is 36149 divisible by 9?
  28. 28.Is 4279 divisible by 7?
  29. 29.Is 126139 divisible by 19?
  30. 30.Is 6606 divisible by 9?
  31. 31.Is 27503 divisible by 7?
  32. 32.Is 19613 divisible by 3?
  33. 33.Is 118697 divisible by 29?
  34. 34.Is 2992 divisible by 8?
  35. 35.Is 97245 divisible by 19?
  36. 36.Is 12250 divisible by 7?
  37. 37.Is 86960 divisible by 13?
  38. 38.Is 44825 divisible by 11?
  39. 39.Is 14856 divisible by 4?
  40. 40.Is 137105 divisible by 23?

Answer key

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

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