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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 389 · 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 126378 divisible by 29?
  2. 2.Is 52887 divisible by 17?
  3. 3.Is 37459 divisible by 23?
  4. 4.Is 13068 divisible by 6?
  5. 5.Is 15605 divisible by 13?
  6. 6.Is 4235 divisible by 7?
  7. 7.Is 133389 divisible by 20?
  8. 8.Is 81018 divisible by 13?
  9. 9.Is 72040 divisible by 11?
  10. 10.Is 18176 divisible by 4?
  11. 11.Is 20036 divisible by 4?
  12. 12.Is 122995 divisible by 19?
  13. 13.Is 31826 divisible by 30?
  14. 14.Is 5348 divisible by 7?
  15. 15.Is 17538 divisible by 6?
  16. 16.Is 20356 divisible by 23?
  17. 17.Is 25472 divisible by 5?
  18. 18.Is 37184 divisible by 8?
  19. 19.Is 35416 divisible by 8?
  20. 20.Is 98887 divisible by 29?
  21. 21.Is 90905 divisible by 13?
  22. 22.Is 76212 divisible by 18?
  23. 23.Is 12433 divisible by 18?
  24. 24.Is 48704 divisible by 9?
  25. 25.Is 1683 divisible by 2?
  26. 26.Is 86471 divisible by 18?
  27. 27.Is 25670 divisible by 9?
  28. 28.Is 20604 divisible by 17?
  29. 29.Is 14721 divisible by 3?
  30. 30.Is 10018 divisible by 7?
  31. 31.Is 30658 divisible by 8?
  32. 32.Is 71497 divisible by 19?
  33. 33.Is 45123 divisible by 24?
  34. 34.Is 36157 divisible by 11?
  35. 35.Is 6890 divisible by 6?
  36. 36.Is 23338 divisible by 7?
  37. 37.Is 34056 divisible by 9?
  38. 38.Is 68839 divisible by 23?
  39. 39.Is 8257 divisible by 2?
  40. 40.Is 3363 divisible by 19?

Answer key

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

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