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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 519 · 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 2260 divisible by 12?
  2. 2.Is 108903 divisible by 20?
  3. 3.Is 36601 divisible by 13?
  4. 4.Is 94758 divisible by 17?
  5. 5.Is 5097 divisible by 24?
  6. 6.Is 6826 divisible by 12?
  7. 7.Is 39990 divisible by 29?
  8. 8.Is 21371 divisible by 13?
  9. 9.Is 41544 divisible by 8?
  10. 10.Is 34597 divisible by 17?
  11. 11.Is 10319 divisible by 2?
  12. 12.Is 21940 divisible by 9?
  13. 13.Is 34445 divisible by 11?
  14. 14.Is 30480 divisible by 30?
  15. 15.Is 34335 divisible by 9?
  16. 16.Is 45570 divisible by 15?
  17. 17.Is 24920 divisible by 5?
  18. 18.Is 20825 divisible by 10?
  19. 19.Is 14280 divisible by 6?
  20. 20.Is 12696 divisible by 3?
  21. 21.Is 46972 divisible by 19?
  22. 22.Is 9675 divisible by 5?
  23. 23.Is 14364 divisible by 19?
  24. 24.Is 27412 divisible by 12?
  25. 25.Is 6348 divisible by 2?
  26. 26.Is 366 divisible by 6?
  27. 27.Is 114 divisible by 3?
  28. 28.Is 34075 divisible by 29?
  29. 29.Is 19530 divisible by 10?
  30. 30.Is 54336 divisible by 12?
  31. 31.Is 8335 divisible by 13?
  32. 32.Is 4958 divisible by 10?
  33. 33.Is 88531 divisible by 19?
  34. 34.Is 37162 divisible by 8?
  35. 35.Is 13156 divisible by 2?
  36. 36.Is 103319 divisible by 20?
  37. 37.Is 19837 divisible by 3?
  38. 38.Is 108402 divisible by 29?
  39. 39.Is 54296 divisible by 10?
  40. 40.Is 92475 divisible by 15?

Answer key

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

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