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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 852 · 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 6838 divisible by 6?
  2. 2.Is 6648 divisible by 12?
  3. 3.Is 28669 divisible by 7?
  4. 4.Is 4772 divisible by 24?
  5. 5.Is 11261 divisible by 2?
  6. 6.Is 17379 divisible by 9?
  7. 7.Is 8553 divisible by 2?
  8. 8.Is 38512 divisible by 8?
  9. 9.Is 9700 divisible by 5?
  10. 10.Is 27900 divisible by 18?
  11. 11.Is 4674 divisible by 2?
  12. 12.Is 12954 divisible by 17?
  13. 13.Is 5817 divisible by 7?
  14. 14.Is 7356 divisible by 6?
  15. 15.Is 33618 divisible by 6?
  16. 16.Is 54813 divisible by 20?
  17. 17.Is 101521 divisible by 23?
  18. 18.Is 62884 divisible by 19?
  19. 19.Is 119289 divisible by 30?
  20. 20.Is 13330 divisible by 3?
  21. 21.Is 71300 divisible by 20?
  22. 22.Is 23297 divisible by 15?
  23. 23.Is 108046 divisible by 30?
  24. 24.Is 30000 divisible by 20?
  25. 25.Is 120834 divisible by 18?
  26. 26.Is 1532 divisible by 18?
  27. 27.Is 22617 divisible by 9?
  28. 28.Is 45690 divisible by 30?
  29. 29.Is 20274 divisible by 3?
  30. 30.Is 41588 divisible by 6?
  31. 31.Is 22220 divisible by 20?
  32. 32.Is 12398 divisible by 4?
  33. 33.Is 11261 divisible by 15?
  34. 34.Is 27719 divisible by 7?
  35. 35.Is 46060 divisible by 13?
  36. 36.Is 15601 divisible by 17?
  37. 37.Is 34248 divisible by 24?
  38. 38.Is 1814 divisible by 12?
  39. 39.Is 50273 divisible by 29?
  40. 40.Is 9135 divisible by 11?

Answer key

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

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