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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 236 · 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 155648 divisible by 30?
  2. 2.Is 33145 divisible by 7?
  3. 3.Is 32359 divisible by 20?
  4. 4.Is 47712 divisible by 12?
  5. 5.Is 105486 divisible by 29?
  6. 6.Is 55160 divisible by 8?
  7. 7.Is 12348 divisible by 6?
  8. 8.Is 148946 divisible by 23?
  9. 9.Is 15485 divisible by 29?
  10. 10.Is 51445 divisible by 8?
  11. 11.Is 4032 divisible by 2?
  12. 12.Is 30769 divisible by 29?
  13. 13.Is 14229 divisible by 17?
  14. 14.Is 26426 divisible by 10?
  15. 15.Is 27574 divisible by 17?
  16. 16.Is 25944 divisible by 6?
  17. 17.Is 43317 divisible by 15?
  18. 18.Is 27024 divisible by 6?
  19. 19.Is 7700 divisible by 5?
  20. 20.Is 55432 divisible by 11?
  21. 21.Is 75624 divisible by 18?
  22. 22.Is 12210 divisible by 5?
  23. 23.Is 94003 divisible by 20?
  24. 24.Is 103060 divisible by 20?
  25. 25.Is 4116 divisible by 3?
  26. 26.Is 67342 divisible by 11?
  27. 27.Is 117601 divisible by 19?
  28. 28.Is 31909 divisible by 17?
  29. 29.Is 69192 divisible by 12?
  30. 30.Is 57014 divisible by 29?
  31. 31.Is 3514 divisible by 7?
  32. 32.Is 39831 divisible by 9?
  33. 33.Is 3085 divisible by 10?
  34. 34.Is 35040 divisible by 30?
  35. 35.Is 20141 divisible by 11?
  36. 36.Is 35637 divisible by 10?
  37. 37.Is 2826 divisible by 2?
  38. 38.Is 3141 divisible by 9?
  39. 39.Is 62592 divisible by 24?
  40. 40.Is 2938 divisible by 13?

Answer key

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

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