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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 746 · 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 167971 divisible by 29?
  2. 2.Is 111378 divisible by 29?
  3. 3.Is 20238 divisible by 3?
  4. 4.Is 50232 divisible by 12?
  5. 5.Is 18387 divisible by 3?
  6. 6.Is 32890 divisible by 11?
  7. 7.Is 12864 divisible by 2?
  8. 8.Is 2502 divisible by 8?
  9. 9.Is 14062 divisible by 7?
  10. 10.Is 14423 divisible by 17?
  11. 11.Is 38376 divisible by 8?
  12. 12.Is 15498 divisible by 4?
  13. 13.Is 7812 divisible by 9?
  14. 14.Is 27344 divisible by 4?
  15. 15.Is 122398 divisible by 19?
  16. 16.Is 5220 divisible by 9?
  17. 17.Is 2025 divisible by 2?
  18. 18.Is 42289 divisible by 13?
  19. 19.Is 26834 divisible by 30?
  20. 20.Is 1835 divisible by 4?
  21. 21.Is 96308 divisible by 19?
  22. 22.Is 31008 divisible by 19?
  23. 23.Is 15739 divisible by 11?
  24. 24.Is 39576 divisible by 12?
  25. 25.Is 32562 divisible by 18?
  26. 26.Is 55489 divisible by 29?
  27. 27.Is 10409 divisible by 2?
  28. 28.Is 38727 divisible by 8?
  29. 29.Is 49271 divisible by 18?
  30. 30.Is 32016 divisible by 17?
  31. 31.Is 2856 divisible by 6?
  32. 32.Is 308 divisible by 7?
  33. 33.Is 19739 divisible by 4?
  34. 34.Is 8529 divisible by 13?
  35. 35.Is 8380 divisible by 12?
  36. 36.Is 10716 divisible by 5?
  37. 37.Is 21651 divisible by 7?
  38. 38.Is 31771 divisible by 11?
  39. 39.Is 83749 divisible by 19?
  40. 40.Is 3738 divisible by 2?

Answer key

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

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