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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 557 · 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 78450 divisible by 30?
  2. 2.Is 21564 divisible by 9?
  3. 3.Is 24095 divisible by 5?
  4. 4.Is 38337 divisible by 8?
  5. 5.Is 132361 divisible by 29?
  6. 6.Is 1440 divisible by 10?
  7. 7.Is 27504 divisible by 6?
  8. 8.Is 113459 divisible by 23?
  9. 9.Is 5539 divisible by 2?
  10. 10.Is 13387 divisible by 2?
  11. 11.Is 7989 divisible by 5?
  12. 12.Is 12432 divisible by 12?
  13. 13.Is 115771 divisible by 19?
  14. 14.Is 64557 divisible by 17?
  15. 15.Is 105260 divisible by 18?
  16. 16.Is 2483 divisible by 17?
  17. 17.Is 897 divisible by 3?
  18. 18.Is 33771 divisible by 6?
  19. 19.Is 29632 divisible by 8?
  20. 20.Is 4614 divisible by 3?
  21. 21.Is 14531 divisible by 12?
  22. 22.Is 49610 divisible by 10?
  23. 23.Is 11820 divisible by 11?
  24. 24.Is 15460 divisible by 9?
  25. 25.Is 2681 divisible by 5?
  26. 26.Is 60896 divisible by 9?
  27. 27.Is 74600 divisible by 20?
  28. 28.Is 41314 divisible by 15?
  29. 29.Is 13320 divisible by 12?
  30. 30.Is 19248 divisible by 3?
  31. 31.Is 26926 divisible by 4?
  32. 32.Is 200604 divisible by 29?
  33. 33.Is 10035 divisible by 15?
  34. 34.Is 53128 divisible by 29?
  35. 35.Is 78468 divisible by 12?
  36. 36.Is 5296 divisible by 4?
  37. 37.Is 55926 divisible by 18?
  38. 38.Is 28646 divisible by 6?
  39. 39.Is 24256 divisible by 7?
  40. 40.Is 101184 divisible by 17?

Answer key

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

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