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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 146 · 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 15991 divisible by 18?
  2. 2.Is 80490 divisible by 15?
  3. 3.Is 10394 divisible by 2?
  4. 4.Is 15888 divisible by 6?
  5. 5.Is 46970 divisible by 17?
  6. 6.Is 3246 divisible by 2?
  7. 7.Is 86880 divisible by 24?
  8. 8.Is 7172 divisible by 11?
  9. 9.Is 17730 divisible by 10?
  10. 10.Is 22152 divisible by 8?
  11. 11.Is 86007 divisible by 29?
  12. 12.Is 2527 divisible by 7?
  13. 13.Is 8883 divisible by 3?
  14. 14.Is 33624 divisible by 6?
  15. 15.Is 5795 divisible by 11?
  16. 16.Is 85251 divisible by 18?
  17. 17.Is 23306 divisible by 12?
  18. 18.Is 10480 divisible by 2?
  19. 19.Is 792 divisible by 3?
  20. 20.Is 62330 divisible by 19?
  21. 21.Is 39020 divisible by 20?
  22. 22.Is 39017 divisible by 6?
  23. 23.Is 62807 divisible by 11?
  24. 24.Is 195630 divisible by 30?
  25. 25.Is 3099 divisible by 17?
  26. 26.Is 2342 divisible by 2?
  27. 27.Is 22547 divisible by 9?
  28. 28.Is 23257 divisible by 13?
  29. 29.Is 54722 divisible by 9?
  30. 30.Is 78890 divisible by 23?
  31. 31.Is 69182 divisible by 11?
  32. 32.Is 26101 divisible by 12?
  33. 33.Is 85159 divisible by 13?
  34. 34.Is 16853 divisible by 4?
  35. 35.Is 59275 divisible by 20?
  36. 36.Is 7356 divisible by 12?
  37. 37.Is 35654 divisible by 18?
  38. 38.Is 85538 divisible by 19?
  39. 39.Is 1647 divisible by 6?
  40. 40.Is 30026 divisible by 7?

Answer key

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

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