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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 968 · 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 14142 divisible by 12?
  2. 2.Is 97052 divisible by 24?
  3. 3.Is 19629 divisible by 9?
  4. 4.Is 76225 divisible by 13?
  5. 5.Is 19155 divisible by 15?
  6. 6.Is 42656 divisible by 8?
  7. 7.Is 10632 divisible by 3?
  8. 8.Is 50904 divisible by 24?
  9. 9.Is 9323 divisible by 13?
  10. 10.Is 24600 divisible by 30?
  11. 11.Is 10860 divisible by 11?
  12. 12.Is 3896 divisible by 5?
  13. 13.Is 21420 divisible by 20?
  14. 14.Is 36990 divisible by 30?
  15. 15.Is 55104 divisible by 12?
  16. 16.Is 13742 divisible by 11?
  17. 17.Is 11439 divisible by 5?
  18. 18.Is 45891 divisible by 11?
  19. 19.Is 22356 divisible by 18?
  20. 20.Is 3821 divisible by 4?
  21. 21.Is 33585 divisible by 5?
  22. 22.Is 151995 divisible by 24?
  23. 23.Is 11073 divisible by 3?
  24. 24.Is 51142 divisible by 8?
  25. 25.Is 23481 divisible by 7?
  26. 26.Is 6084 divisible by 5?
  27. 27.Is 126147 divisible by 23?
  28. 28.Is 13080 divisible by 20?
  29. 29.Is 43198 divisible by 9?
  30. 30.Is 10194 divisible by 5?
  31. 31.Is 39684 divisible by 12?
  32. 32.Is 1258 divisible by 17?
  33. 33.Is 81212 divisible by 17?
  34. 34.Is 26244 divisible by 6?
  35. 35.Is 31694 divisible by 23?
  36. 36.Is 45995 divisible by 23?
  37. 37.Is 29494 divisible by 30?
  38. 38.Is 75636 divisible by 30?
  39. 39.Is 1171 divisible by 2?
  40. 40.Is 133078 divisible by 23?

Answer key

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

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