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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 987 · 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 47175 divisible by 15?
  2. 2.Is 6201 divisible by 2?
  3. 3.Is 61428 divisible by 12?
  4. 4.Is 107719 divisible by 23?
  5. 5.Is 7739 divisible by 11?
  6. 6.Is 26204 divisible by 9?
  7. 7.Is 11821 divisible by 3?
  8. 8.Is 11120 divisible by 20?
  9. 9.Is 17737 divisible by 10?
  10. 10.Is 105844 divisible by 30?
  11. 11.Is 2360 divisible by 15?
  12. 12.Is 73953 divisible by 23?
  13. 13.Is 6725 divisible by 20?
  14. 14.Is 14242 divisible by 4?
  15. 15.Is 16295 divisible by 29?
  16. 16.Is 120140 divisible by 20?
  17. 17.Is 61270 divisible by 11?
  18. 18.Is 45135 divisible by 9?
  19. 19.Is 110239 divisible by 18?
  20. 20.Is 165072 divisible by 24?
  21. 21.Is 24605 divisible by 7?
  22. 22.Is 864 divisible by 10?
  23. 23.Is 53447 divisible by 17?
  24. 24.Is 75221 divisible by 19?
  25. 25.Is 48001 divisible by 23?
  26. 26.Is 71977 divisible by 12?
  27. 27.Is 26530 divisible by 5?
  28. 28.Is 95970 divisible by 30?
  29. 29.Is 14768 divisible by 4?
  30. 30.Is 51892 divisible by 10?
  31. 31.Is 9096 divisible by 12?
  32. 32.Is 120504 divisible by 24?
  33. 33.Is 149100 divisible by 29?
  34. 34.Is 4693 divisible by 5?
  35. 35.Is 114685 divisible by 24?
  36. 36.Is 3684 divisible by 12?
  37. 37.Is 44018 divisible by 13?
  38. 38.Is 2330 divisible by 2?
  39. 39.Is 79123 divisible by 23?
  40. 40.Is 1336 divisible by 2?

Answer key

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

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