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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 289 · 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 128232 divisible by 19?
  2. 2.Is 52783 divisible by 10?
  3. 3.Is 70318 divisible by 11?
  4. 4.Is 3744 divisible by 8?
  5. 5.Is 143681 divisible by 23?
  6. 6.Is 3356 divisible by 6?
  7. 7.Is 80733 divisible by 24?
  8. 8.Is 46914 divisible by 13?
  9. 9.Is 16245 divisible by 19?
  10. 10.Is 7482 divisible by 6?
  11. 11.Is 23076 divisible by 12?
  12. 12.Is 23325 divisible by 15?
  13. 13.Is 26273 divisible by 17?
  14. 14.Is 112480 divisible by 19?
  15. 15.Is 15885 divisible by 9?
  16. 16.Is 12864 divisible by 8?
  17. 17.Is 14133 divisible by 3?
  18. 18.Is 118128 divisible by 23?
  19. 19.Is 127224 divisible by 19?
  20. 20.Is 45795 divisible by 8?
  21. 21.Is 20562 divisible by 6?
  22. 22.Is 21516 divisible by 12?
  23. 23.Is 52766 divisible by 15?
  24. 24.Is 35725 divisible by 6?
  25. 25.Is 23417 divisible by 12?
  26. 26.Is 29979 divisible by 9?
  27. 27.Is 19952 divisible by 6?
  28. 28.Is 43992 divisible by 13?
  29. 29.Is 10571 divisible by 2?
  30. 30.Is 10486 divisible by 3?
  31. 31.Is 18857 divisible by 8?
  32. 32.Is 166567 divisible by 24?
  33. 33.Is 11736 divisible by 12?
  34. 34.Is 46672 divisible by 17?
  35. 35.Is 101310 divisible by 15?
  36. 36.Is 540 divisible by 2?
  37. 37.Is 17556 divisible by 12?
  38. 38.Is 28840 divisible by 8?
  39. 39.Is 459 divisible by 9?
  40. 40.Is 133929 divisible by 23?

Answer key

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

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