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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 755 · 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 18284 divisible by 7?
  2. 2.Is 18278 divisible by 5?
  3. 3.Is 15090 divisible by 15?
  4. 4.Is 1873 divisible by 2?
  5. 5.Is 50998 divisible by 23?
  6. 6.Is 58450 divisible by 9?
  7. 7.Is 27274 divisible by 8?
  8. 8.Is 8522 divisible by 4?
  9. 9.Is 25386 divisible by 17?
  10. 10.Is 58642 divisible by 19?
  11. 11.Is 121921 divisible by 24?
  12. 12.Is 13520 divisible by 10?
  13. 13.Is 3755 divisible by 5?
  14. 14.Is 76473 divisible by 11?
  15. 15.Is 47796 divisible by 12?
  16. 16.Is 81835 divisible by 13?
  17. 17.Is 15264 divisible by 3?
  18. 18.Is 55157 divisible by 10?
  19. 19.Is 18989 divisible by 15?
  20. 20.Is 9955 divisible by 3?
  21. 21.Is 119618 divisible by 29?
  22. 22.Is 72142 divisible by 20?
  23. 23.Is 68858 divisible by 15?
  24. 24.Is 25995 divisible by 12?
  25. 25.Is 12799 divisible by 3?
  26. 26.Is 55856 divisible by 8?
  27. 27.Is 27929 divisible by 8?
  28. 28.Is 7672 divisible by 8?
  29. 29.Is 73716 divisible by 12?
  30. 30.Is 21326 divisible by 11?
  31. 31.Is 3785 divisible by 2?
  32. 32.Is 5756 divisible by 5?
  33. 33.Is 16442 divisible by 9?
  34. 34.Is 147864 divisible by 24?
  35. 35.Is 3661 divisible by 7?
  36. 36.Is 12967 divisible by 11?
  37. 37.Is 52632 divisible by 17?
  38. 38.Is 53550 divisible by 10?
  39. 39.Is 20767 divisible by 3?
  40. 40.Is 12912 divisible by 12?

Answer key

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

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