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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 653 · 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 20059 divisible by 13?
  2. 2.Is 67740 divisible by 12?
  3. 3.Is 7592 divisible by 23?
  4. 4.Is 13251 divisible by 11?
  5. 5.Is 19487 divisible by 3?
  6. 6.Is 28740 divisible by 20?
  7. 7.Is 25680 divisible by 5?
  8. 8.Is 12937 divisible by 17?
  9. 9.Is 44590 divisible by 10?
  10. 10.Is 26047 divisible by 7?
  11. 11.Is 12422 divisible by 10?
  12. 12.Is 52240 divisible by 13?
  13. 13.Is 60444 divisible by 9?
  14. 14.Is 6741 divisible by 9?
  15. 15.Is 21982 divisible by 10?
  16. 16.Is 75696 divisible by 12?
  17. 17.Is 19020 divisible by 6?
  18. 18.Is 20400 divisible by 15?
  19. 19.Is 102855 divisible by 15?
  20. 20.Is 10941 divisible by 7?
  21. 21.Is 37538 divisible by 6?
  22. 22.Is 27605 divisible by 23?
  23. 23.Is 47423 divisible by 9?
  24. 24.Is 28894 divisible by 11?
  25. 25.Is 108400 divisible by 20?
  26. 26.Is 96532 divisible by 17?
  27. 27.Is 11988 divisible by 2?
  28. 28.Is 21464 divisible by 8?
  29. 29.Is 5914 divisible by 2?
  30. 30.Is 66446 divisible by 18?
  31. 31.Is 15405 divisible by 3?
  32. 32.Is 1093 divisible by 10?
  33. 33.Is 17391 divisible by 5?
  34. 34.Is 3900 divisible by 19?
  35. 35.Is 132122 divisible by 24?
  36. 36.Is 21058 divisible by 6?
  37. 37.Is 40919 divisible by 29?
  38. 38.Is 41473 divisible by 15?
  39. 39.Is 30769 divisible by 15?
  40. 40.Is 112816 divisible by 30?

Answer key

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

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