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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 581 · 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 21600 divisible by 5?
  2. 2.Is 18360 divisible by 15?
  3. 3.Is 33615 divisible by 7?
  4. 4.Is 83899 divisible by 15?
  5. 5.Is 12705 divisible by 29?
  6. 6.Is 29070 divisible by 5?
  7. 7.Is 51634 divisible by 11?
  8. 8.Is 139055 divisible by 29?
  9. 9.Is 1620 divisible by 5?
  10. 10.Is 9660 divisible by 15?
  11. 11.Is 6042 divisible by 4?
  12. 12.Is 74617 divisible by 29?
  13. 13.Is 163224 divisible by 24?
  14. 14.Is 1872 divisible by 18?
  15. 15.Is 31635 divisible by 15?
  16. 16.Is 44206 divisible by 13?
  17. 17.Is 51326 divisible by 11?
  18. 18.Is 19427 divisible by 11?
  19. 19.Is 5899 divisible by 5?
  20. 20.Is 87980 divisible by 20?
  21. 21.Is 33768 divisible by 18?
  22. 22.Is 22600 divisible by 8?
  23. 23.Is 58708 divisible by 12?
  24. 24.Is 33807 divisible by 5?
  25. 25.Is 3111 divisible by 4?
  26. 26.Is 168513 divisible by 30?
  27. 27.Is 27694 divisible by 20?
  28. 28.Is 31822 divisible by 20?
  29. 29.Is 66191 divisible by 20?
  30. 30.Is 85120 divisible by 19?
  31. 31.Is 82921 divisible by 13?
  32. 32.Is 10142 divisible by 7?
  33. 33.Is 41874 divisible by 6?
  34. 34.Is 73773 divisible by 19?
  35. 35.Is 9392 divisible by 19?
  36. 36.Is 13005 divisible by 6?
  37. 37.Is 27688 divisible by 4?
  38. 38.Is 23686 divisible by 20?
  39. 39.Is 4358 divisible by 6?
  40. 40.Is 83076 divisible by 23?

Answer key

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

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