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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 791 · 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 38196 divisible by 12?
  2. 2.Is 11432 divisible by 8?
  3. 3.Is 54529 divisible by 9?
  4. 4.Is 102085 divisible by 23?
  5. 5.Is 9265 divisible by 2?
  6. 6.Is 6155 divisible by 3?
  7. 7.Is 6877 divisible by 13?
  8. 8.Is 136560 divisible by 20?
  9. 9.Is 21996 divisible by 4?
  10. 10.Is 37734 divisible by 6?
  11. 11.Is 50301 divisible by 10?
  12. 12.Is 21835 divisible by 5?
  13. 13.Is 2877 divisible by 2?
  14. 14.Is 13533 divisible by 2?
  15. 15.Is 20507 divisible by 6?
  16. 16.Is 11621 divisible by 8?
  17. 17.Is 9449 divisible by 4?
  18. 18.Is 3096 divisible by 3?
  19. 19.Is 110006 divisible by 29?
  20. 20.Is 7988 divisible by 3?
  21. 21.Is 30363 divisible by 17?
  22. 22.Is 170382 divisible by 29?
  23. 23.Is 33828 divisible by 6?
  24. 24.Is 7434 divisible by 2?
  25. 25.Is 23095 divisible by 5?
  26. 26.Is 24696 divisible by 6?
  27. 27.Is 156239 divisible by 23?
  28. 28.Is 15023 divisible by 3?
  29. 29.Is 150144 divisible by 24?
  30. 30.Is 40368 divisible by 10?
  31. 31.Is 29930 divisible by 24?
  32. 32.Is 5612 divisible by 4?
  33. 33.Is 13418 divisible by 2?
  34. 34.Is 20902 divisible by 7?
  35. 35.Is 7657 divisible by 15?
  36. 36.Is 27489 divisible by 17?
  37. 37.Is 35298 divisible by 18?
  38. 38.Is 81447 divisible by 17?
  39. 39.Is 101040 divisible by 24?
  40. 40.Is 26402 divisible by 15?

Answer key

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

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