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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 67 · 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 22755 divisible by 4?
  2. 2.Is 96744 divisible by 19?
  3. 3.Is 37946 divisible by 8?
  4. 4.Is 12540 divisible by 10?
  5. 5.Is 178157 divisible by 30?
  6. 6.Is 19056 divisible by 24?
  7. 7.Is 109942 divisible by 17?
  8. 8.Is 15855 divisible by 5?
  9. 9.Is 12493 divisible by 2?
  10. 10.Is 39375 divisible by 15?
  11. 11.Is 7367 divisible by 2?
  12. 12.Is 48432 divisible by 8?
  13. 13.Is 195941 divisible by 29?
  14. 14.Is 25075 divisible by 5?
  15. 15.Is 89300 divisible by 19?
  16. 16.Is 101069 divisible by 17?
  17. 17.Is 22464 divisible by 10?
  18. 18.Is 3547 divisible by 3?
  19. 19.Is 53083 divisible by 19?
  20. 20.Is 6062 divisible by 4?
  21. 21.Is 66989 divisible by 29?
  22. 22.Is 19697 divisible by 3?
  23. 23.Is 8779 divisible by 13?
  24. 24.Is 10752 divisible by 7?
  25. 25.Is 1287 divisible by 3?
  26. 26.Is 12264 divisible by 2?
  27. 27.Is 23798 divisible by 17?
  28. 28.Is 48813 divisible by 17?
  29. 29.Is 41114 divisible by 20?
  30. 30.Is 27765 divisible by 29?
  31. 31.Is 15019 divisible by 4?
  32. 32.Is 3069 divisible by 2?
  33. 33.Is 88942 divisible by 20?
  34. 34.Is 61915 divisible by 29?
  35. 35.Is 10927 divisible by 7?
  36. 36.Is 38087 divisible by 29?
  37. 37.Is 17588 divisible by 4?
  38. 38.Is 37062 divisible by 18?
  39. 39.Is 106852 divisible by 17?
  40. 40.Is 7804 divisible by 8?

Answer key

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

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