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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 209 · 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 190153 divisible by 29?
  2. 2.Is 33342 divisible by 6?
  3. 3.Is 14020 divisible by 7?
  4. 4.Is 82360 divisible by 29?
  5. 5.Is 18330 divisible by 6?
  6. 6.Is 15379 divisible by 4?
  7. 7.Is 6048 divisible by 9?
  8. 8.Is 95960 divisible by 20?
  9. 9.Is 23868 divisible by 4?
  10. 10.Is 57301 divisible by 20?
  11. 11.Is 125304 divisible by 23?
  12. 12.Is 33198 divisible by 6?
  13. 13.Is 88220 divisible by 20?
  14. 14.Is 71325 divisible by 11?
  15. 15.Is 190710 divisible by 30?
  16. 16.Is 125080 divisible by 20?
  17. 17.Is 49588 divisible by 23?
  18. 18.Is 126138 divisible by 30?
  19. 19.Is 3894 divisible by 10?
  20. 20.Is 225 divisible by 4?
  21. 21.Is 96656 divisible by 15?
  22. 22.Is 20279 divisible by 7?
  23. 23.Is 12747 divisible by 11?
  24. 24.Is 38993 divisible by 19?
  25. 25.Is 36867 divisible by 9?
  26. 26.Is 18146 divisible by 30?
  27. 27.Is 12825 divisible by 10?
  28. 28.Is 281 divisible by 8?
  29. 29.Is 85882 divisible by 15?
  30. 30.Is 137080 divisible by 23?
  31. 31.Is 18521 divisible by 29?
  32. 32.Is 117240 divisible by 20?
  33. 33.Is 113059 divisible by 18?
  34. 34.Is 45073 divisible by 8?
  35. 35.Is 71652 divisible by 12?
  36. 36.Is 38307 divisible by 17?
  37. 37.Is 94452 divisible by 20?
  38. 38.Is 103252 divisible by 20?
  39. 39.Is 38646 divisible by 6?
  40. 40.Is 79800 divisible by 24?

Answer key

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

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