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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 229 · 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 31745 divisible by 8?
  2. 2.Is 3938 divisible by 2?
  3. 3.Is 106464 divisible by 30?
  4. 4.Is 21371 divisible by 7?
  5. 5.Is 9005 divisible by 7?
  6. 6.Is 37789 divisible by 6?
  7. 7.Is 130169 divisible by 19?
  8. 8.Is 61729 divisible by 9?
  9. 9.Is 73560 divisible by 20?
  10. 10.Is 9200 divisible by 5?
  11. 11.Is 115676 divisible by 19?
  12. 12.Is 19994 divisible by 4?
  13. 13.Is 43752 divisible by 13?
  14. 14.Is 2679 divisible by 29?
  15. 15.Is 3591 divisible by 7?
  16. 16.Is 123073 divisible by 23?
  17. 17.Is 55720 divisible by 13?
  18. 18.Is 77856 divisible by 12?
  19. 19.Is 34665 divisible by 5?
  20. 20.Is 40638 divisible by 6?
  21. 21.Is 17281 divisible by 5?
  22. 22.Is 35240 divisible by 10?
  23. 23.Is 117300 divisible by 20?
  24. 24.Is 16752 divisible by 9?
  25. 25.Is 70884 divisible by 12?
  26. 26.Is 76245 divisible by 15?
  27. 27.Is 58001 divisible by 13?
  28. 28.Is 13136 divisible by 7?
  29. 29.Is 21720 divisible by 30?
  30. 30.Is 39652 divisible by 13?
  31. 31.Is 147777 divisible by 23?
  32. 32.Is 20162 divisible by 23?
  33. 33.Is 18800 divisible by 18?
  34. 34.Is 9756 divisible by 11?
  35. 35.Is 4295 divisible by 6?
  36. 36.Is 14745 divisible by 3?
  37. 37.Is 120774 divisible by 20?
  38. 38.Is 9310 divisible by 23?
  39. 39.Is 3301 divisible by 2?
  40. 40.Is 47880 divisible by 24?

Answer key

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

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