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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 37 · 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 41503 divisible by 23?
  2. 2.Is 29248 divisible by 8?
  3. 3.Is 24288 divisible by 11?
  4. 4.Is 115640 divisible by 23?
  5. 5.Is 30924 divisible by 6?
  6. 6.Is 38563 divisible by 8?
  7. 7.Is 144 divisible by 6?
  8. 8.Is 54954 divisible by 9?
  9. 9.Is 6180 divisible by 2?
  10. 10.Is 42328 divisible by 8?
  11. 11.Is 40732 divisible by 17?
  12. 12.Is 12095 divisible by 5?
  13. 13.Is 33881 divisible by 17?
  14. 14.Is 34295 divisible by 5?
  15. 15.Is 7700 divisible by 10?
  16. 16.Is 2367 divisible by 3?
  17. 17.Is 6107 divisible by 5?
  18. 18.Is 35544 divisible by 7?
  19. 19.Is 153420 divisible by 30?
  20. 20.Is 13200 divisible by 2?
  21. 21.Is 34743 divisible by 7?
  22. 22.Is 150990 divisible by 30?
  23. 23.Is 23737 divisible by 5?
  24. 24.Is 15876 divisible by 5?
  25. 25.Is 16974 divisible by 9?
  26. 26.Is 1571 divisible by 3?
  27. 27.Is 10016 divisible by 4?
  28. 28.Is 2110 divisible by 20?
  29. 29.Is 91341 divisible by 17?
  30. 30.Is 46182 divisible by 10?
  31. 31.Is 42459 divisible by 7?
  32. 32.Is 69268 divisible by 30?
  33. 33.Is 46830 divisible by 30?
  34. 34.Is 130680 divisible by 30?
  35. 35.Is 193279 divisible by 29?
  36. 36.Is 14768 divisible by 12?
  37. 37.Is 1754 divisible by 2?
  38. 38.Is 3561 divisible by 4?
  39. 39.Is 178234 divisible by 29?
  40. 40.Is 67213 divisible by 24?

Answer key

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

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