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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 269 · 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 33001 divisible by 5?
  2. 2.Is 91864 divisible by 17?
  3. 3.Is 181560 divisible by 30?
  4. 4.Is 43116 divisible by 7?
  5. 5.Is 4110 divisible by 3?
  6. 6.Is 34210 divisible by 5?
  7. 7.Is 26100 divisible by 6?
  8. 8.Is 69666 divisible by 30?
  9. 9.Is 7728 divisible by 8?
  10. 10.Is 4153 divisible by 6?
  11. 11.Is 52236 divisible by 29?
  12. 12.Is 18424 divisible by 11?
  13. 13.Is 10224 divisible by 12?
  14. 14.Is 120978 divisible by 18?
  15. 15.Is 917 divisible by 2?
  16. 16.Is 76656 divisible by 24?
  17. 17.Is 33793 divisible by 5?
  18. 18.Is 40800 divisible by 6?
  19. 19.Is 85819 divisible by 13?
  20. 20.Is 55848 divisible by 11?
  21. 21.Is 47159 divisible by 7?
  22. 22.Is 41862 divisible by 29?
  23. 23.Is 18850 divisible by 5?
  24. 24.Is 80546 divisible by 17?
  25. 25.Is 6060 divisible by 2?
  26. 26.Is 24895 divisible by 11?
  27. 27.Is 48330 divisible by 18?
  28. 28.Is 144999 divisible by 24?
  29. 29.Is 38000 divisible by 13?
  30. 30.Is 39049 divisible by 7?
  31. 31.Is 80682 divisible by 12?
  32. 32.Is 17029 divisible by 8?
  33. 33.Is 673 divisible by 2?
  34. 34.Is 8287 divisible by 23?
  35. 35.Is 143521 divisible by 29?
  36. 36.Is 158831 divisible by 24?
  37. 37.Is 6782 divisible by 3?
  38. 38.Is 8683 divisible by 24?
  39. 39.Is 41959 divisible by 9?
  40. 40.Is 121961 divisible by 29?

Answer key

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

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