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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 199 · 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 19618 divisible by 9?
  2. 2.Is 3019 divisible by 20?
  3. 3.Is 66618 divisible by 19?
  4. 4.Is 20361 divisible by 4?
  5. 5.Is 95167 divisible by 17?
  6. 6.Is 29079 divisible by 5?
  7. 7.Is 18049 divisible by 9?
  8. 8.Is 38244 divisible by 19?
  9. 9.Is 77740 divisible by 13?
  10. 10.Is 29017 divisible by 13?
  11. 11.Is 2713 divisible by 3?
  12. 12.Is 111810 divisible by 30?
  13. 13.Is 13638 divisible by 8?
  14. 14.Is 4692 divisible by 10?
  15. 15.Is 80500 divisible by 20?
  16. 16.Is 2373 divisible by 3?
  17. 17.Is 6309 divisible by 9?
  18. 18.Is 49120 divisible by 8?
  19. 19.Is 16078 divisible by 6?
  20. 20.Is 5532 divisible by 8?
  21. 21.Is 81000 divisible by 15?
  22. 22.Is 47320 divisible by 8?
  23. 23.Is 101765 divisible by 19?
  24. 24.Is 130640 divisible by 23?
  25. 25.Is 202960 divisible by 29?
  26. 26.Is 1755 divisible by 3?
  27. 27.Is 48741 divisible by 11?
  28. 28.Is 12920 divisible by 8?
  29. 29.Is 33547 divisible by 7?
  30. 30.Is 43531 divisible by 12?
  31. 31.Is 8147 divisible by 4?
  32. 32.Is 40650 divisible by 6?
  33. 33.Is 20247 divisible by 8?
  34. 34.Is 43890 divisible by 10?
  35. 35.Is 39031 divisible by 23?
  36. 36.Is 13900 divisible by 12?
  37. 37.Is 2362 divisible by 2?
  38. 38.Is 160463 divisible by 23?
  39. 39.Is 27132 divisible by 6?
  40. 40.Is 43061 divisible by 30?

Answer key

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

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