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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 522 · 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 25415 divisible by 5?
  2. 2.Is 20185 divisible by 3?
  3. 3.Is 119538 divisible by 18?
  4. 4.Is 33030 divisible by 9?
  5. 5.Is 10362 divisible by 3?
  6. 6.Is 21790 divisible by 9?
  7. 7.Is 2632 divisible by 2?
  8. 8.Is 9698 divisible by 29?
  9. 9.Is 18044 divisible by 17?
  10. 10.Is 31361 divisible by 11?
  11. 11.Is 124763 divisible by 20?
  12. 12.Is 4339 divisible by 3?
  13. 13.Is 34141 divisible by 5?
  14. 14.Is 1020 divisible by 3?
  15. 15.Is 40642 divisible by 20?
  16. 16.Is 109080 divisible by 30?
  17. 17.Is 14456 divisible by 7?
  18. 18.Is 57926 divisible by 29?
  19. 19.Is 65550 divisible by 10?
  20. 20.Is 172422 divisible by 29?
  21. 21.Is 30979 divisible by 30?
  22. 22.Is 356 divisible by 5?
  23. 23.Is 157620 divisible by 29?
  24. 24.Is 31046 divisible by 20?
  25. 25.Is 6783 divisible by 7?
  26. 26.Is 199620 divisible by 30?
  27. 27.Is 9031 divisible by 2?
  28. 28.Is 12178 divisible by 4?
  29. 29.Is 760 divisible by 3?
  30. 30.Is 13212 divisible by 6?
  31. 31.Is 5564 divisible by 4?
  32. 32.Is 49880 divisible by 29?
  33. 33.Is 102192 divisible by 24?
  34. 34.Is 107448 divisible by 24?
  35. 35.Is 38820 divisible by 12?
  36. 36.Is 80286 divisible by 20?
  37. 37.Is 37472 divisible by 11?
  38. 38.Is 7452 divisible by 10?
  39. 39.Is 36812 divisible by 23?
  40. 40.Is 38142 divisible by 13?

Answer key

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

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