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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 525 · 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 112968 divisible by 24?
  2. 2.Is 49700 divisible by 10?
  3. 3.Is 76728 divisible by 17?
  4. 4.Is 75816 divisible by 13?
  5. 5.Is 22872 divisible by 12?
  6. 6.Is 42240 divisible by 8?
  7. 7.Is 50890 divisible by 9?
  8. 8.Is 9866 divisible by 7?
  9. 9.Is 8676 divisible by 6?
  10. 10.Is 49302 divisible by 9?
  11. 11.Is 42112 divisible by 7?
  12. 12.Is 22942 divisible by 24?
  13. 13.Is 138024 divisible by 24?
  14. 14.Is 8323 divisible by 10?
  15. 15.Is 75873 divisible by 12?
  16. 16.Is 901 divisible by 5?
  17. 17.Is 10886 divisible by 11?
  18. 18.Is 123101 divisible by 19?
  19. 19.Is 72816 divisible by 29?
  20. 20.Is 28620 divisible by 20?
  21. 21.Is 112591 divisible by 17?
  22. 22.Is 14898 divisible by 3?
  23. 23.Is 12285 divisible by 15?
  24. 24.Is 28807 divisible by 5?
  25. 25.Is 22703 divisible by 18?
  26. 26.Is 187688 divisible by 29?
  27. 27.Is 22408 divisible by 4?
  28. 28.Is 42950 divisible by 8?
  29. 29.Is 44376 divisible by 12?
  30. 30.Is 174620 divisible by 30?
  31. 31.Is 7399 divisible by 8?
  32. 32.Is 68790 divisible by 23?
  33. 33.Is 39241 divisible by 9?
  34. 34.Is 120023 divisible by 19?
  35. 35.Is 23943 divisible by 11?
  36. 36.Is 65963 divisible by 17?
  37. 37.Is 110479 divisible by 19?
  38. 38.Is 26240 divisible by 8?
  39. 39.Is 99014 divisible by 15?
  40. 40.Is 43057 divisible by 7?

Answer key

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

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