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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 173 · 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 17513 divisible by 18?
  2. 2.Is 38088 divisible by 18?
  3. 3.Is 26334 divisible by 19?
  4. 4.Is 36133 divisible by 8?
  5. 5.Is 55055 divisible by 13?
  6. 6.Is 11576 divisible by 7?
  7. 7.Is 36800 divisible by 10?
  8. 8.Is 935 divisible by 5?
  9. 9.Is 16570 divisible by 5?
  10. 10.Is 20675 divisible by 5?
  11. 11.Is 72096 divisible by 24?
  12. 12.Is 98832 divisible by 29?
  13. 13.Is 5103 divisible by 2?
  14. 14.Is 13784 divisible by 8?
  15. 15.Is 114720 divisible by 20?
  16. 16.Is 15387 divisible by 4?
  17. 17.Is 70876 divisible by 17?
  18. 18.Is 116946 divisible by 18?
  19. 19.Is 12507 divisible by 5?
  20. 20.Is 35010 divisible by 10?
  21. 21.Is 6455 divisible by 9?
  22. 22.Is 10410 divisible by 10?
  23. 23.Is 81133 divisible by 13?
  24. 24.Is 15493 divisible by 4?
  25. 25.Is 3288 divisible by 15?
  26. 26.Is 105133 divisible by 23?
  27. 27.Is 1593 divisible by 2?
  28. 28.Is 91815 divisible by 23?
  29. 29.Is 37419 divisible by 7?
  30. 30.Is 126179 divisible by 29?
  31. 31.Is 110952 divisible by 18?
  32. 32.Is 4782 divisible by 2?
  33. 33.Is 4499 divisible by 17?
  34. 34.Is 89041 divisible by 30?
  35. 35.Is 9677 divisible by 5?
  36. 36.Is 19130 divisible by 24?
  37. 37.Is 18016 divisible by 10?
  38. 38.Is 19291 divisible by 4?
  39. 39.Is 14366 divisible by 11?
  40. 40.Is 69603 divisible by 15?

Answer key

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

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