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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 139 · 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 87580 divisible by 20?
  2. 2.Is 37625 divisible by 7?
  3. 3.Is 15360 divisible by 10?
  4. 4.Is 19895 divisible by 3?
  5. 5.Is 20645 divisible by 6?
  6. 6.Is 59371 divisible by 15?
  7. 7.Is 82064 divisible by 23?
  8. 8.Is 24361 divisible by 15?
  9. 9.Is 26466 divisible by 6?
  10. 10.Is 73088 divisible by 29?
  11. 11.Is 51720 divisible by 20?
  12. 12.Is 49464 divisible by 8?
  13. 13.Is 21826 divisible by 7?
  14. 14.Is 13404 divisible by 6?
  15. 15.Is 1849 divisible by 6?
  16. 16.Is 47908 divisible by 29?
  17. 17.Is 19888 divisible by 11?
  18. 18.Is 315 divisible by 4?
  19. 19.Is 154377 divisible by 24?
  20. 20.Is 591 divisible by 11?
  21. 21.Is 1722 divisible by 7?
  22. 22.Is 11851 divisible by 7?
  23. 23.Is 58325 divisible by 9?
  24. 24.Is 26595 divisible by 7?
  25. 25.Is 55784 divisible by 20?
  26. 26.Is 12333 divisible by 3?
  27. 27.Is 121014 divisible by 18?
  28. 28.Is 28935 divisible by 9?
  29. 29.Is 29917 divisible by 6?
  30. 30.Is 81342 divisible by 18?
  31. 31.Is 108779 divisible by 29?
  32. 32.Is 52400 divisible by 10?
  33. 33.Is 26911 divisible by 17?
  34. 34.Is 141665 divisible by 29?
  35. 35.Is 111970 divisible by 18?
  36. 36.Is 6806 divisible by 5?
  37. 37.Is 46800 divisible by 8?
  38. 38.Is 30042 divisible by 9?
  39. 39.Is 15295 divisible by 3?
  40. 40.Is 66340 divisible by 10?

Answer key

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

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