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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 888 · 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 41054 divisible by 30?
  2. 2.Is 83045 divisible by 20?
  3. 3.Is 90076 divisible by 15?
  4. 4.Is 6888 divisible by 5?
  5. 5.Is 11736 divisible by 2?
  6. 6.Is 10423 divisible by 2?
  7. 7.Is 63954 divisible by 11?
  8. 8.Is 11475 divisible by 4?
  9. 9.Is 103066 divisible by 29?
  10. 10.Is 7912 divisible by 23?
  11. 11.Is 6124 divisible by 9?
  12. 12.Is 45839 divisible by 23?
  13. 13.Is 111319 divisible by 30?
  14. 14.Is 27738 divisible by 23?
  15. 15.Is 674 divisible by 30?
  16. 16.Is 112880 divisible by 20?
  17. 17.Is 17790 divisible by 10?
  18. 18.Is 90125 divisible by 20?
  19. 19.Is 51372 divisible by 12?
  20. 20.Is 21461 divisible by 11?
  21. 21.Is 66599 divisible by 30?
  22. 22.Is 10206 divisible by 3?
  23. 23.Is 89452 divisible by 19?
  24. 24.Is 5746 divisible by 6?
  25. 25.Is 8849 divisible by 17?
  26. 26.Is 10332 divisible by 18?
  27. 27.Is 8273 divisible by 2?
  28. 28.Is 10768 divisible by 8?
  29. 29.Is 135633 divisible by 29?
  30. 30.Is 18603 divisible by 11?
  31. 31.Is 22680 divisible by 7?
  32. 32.Is 13205 divisible by 19?
  33. 33.Is 17145 divisible by 3?
  34. 34.Is 8574 divisible by 4?
  35. 35.Is 134004 divisible by 24?
  36. 36.Is 38137 divisible by 11?
  37. 37.Is 16676 divisible by 11?
  38. 38.Is 32973 divisible by 10?
  39. 39.Is 46085 divisible by 12?
  40. 40.Is 680 divisible by 3?

Answer key

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

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