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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 377 · 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 191917 divisible by 30?
  2. 2.Is 8170 divisible by 4?
  3. 3.Is 37360 divisible by 15?
  4. 4.Is 69840 divisible by 24?
  5. 5.Is 125038 divisible by 30?
  6. 6.Is 73499 divisible by 19?
  7. 7.Is 4757 divisible by 7?
  8. 8.Is 19909 divisible by 5?
  9. 9.Is 14858 divisible by 6?
  10. 10.Is 69796 divisible by 13?
  11. 11.Is 1210 divisible by 11?
  12. 12.Is 71592 divisible by 19?
  13. 13.Is 16225 divisible by 5?
  14. 14.Is 20303 divisible by 6?
  15. 15.Is 25787 divisible by 9?
  16. 16.Is 16324 divisible by 11?
  17. 17.Is 52720 divisible by 29?
  18. 18.Is 11922 divisible by 4?
  19. 19.Is 10095 divisible by 6?
  20. 20.Is 32858 divisible by 7?
  21. 21.Is 43690 divisible by 19?
  22. 22.Is 1694 divisible by 7?
  23. 23.Is 41525 divisible by 30?
  24. 24.Is 17267 divisible by 20?
  25. 25.Is 12292 divisible by 3?
  26. 26.Is 39169 divisible by 13?
  27. 27.Is 27408 divisible by 4?
  28. 28.Is 6590 divisible by 10?
  29. 29.Is 43911 divisible by 7?
  30. 30.Is 38784 divisible by 12?
  31. 31.Is 45846 divisible by 20?
  32. 32.Is 34767 divisible by 10?
  33. 33.Is 37880 divisible by 20?
  34. 34.Is 24157 divisible by 7?
  35. 35.Is 15400 divisible by 20?
  36. 36.Is 35109 divisible by 6?
  37. 37.Is 16783 divisible by 3?
  38. 38.Is 117818 divisible by 19?
  39. 39.Is 173110 divisible by 29?
  40. 40.Is 20455 divisible by 11?

Answer key

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

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