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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 122 · 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 10602 divisible by 19?
  2. 2.Is 37138 divisible by 17?
  3. 3.Is 103063 divisible by 23?
  4. 4.Is 53945 divisible by 11?
  5. 5.Is 42256 divisible by 8?
  6. 6.Is 4752 divisible by 6?
  7. 7.Is 33880 divisible by 20?
  8. 8.Is 27364 divisible by 5?
  9. 9.Is 20684 divisible by 3?
  10. 10.Is 47022 divisible by 24?
  11. 11.Is 16901 divisible by 3?
  12. 12.Is 100776 divisible by 18?
  13. 13.Is 15590 divisible by 4?
  14. 14.Is 4987 divisible by 5?
  15. 15.Is 10615 divisible by 2?
  16. 16.Is 3569 divisible by 5?
  17. 17.Is 17128 divisible by 4?
  18. 18.Is 34614 divisible by 5?
  19. 19.Is 8884 divisible by 7?
  20. 20.Is 32062 divisible by 19?
  21. 21.Is 9158 divisible by 19?
  22. 22.Is 116077 divisible by 18?
  23. 23.Is 38814 divisible by 6?
  24. 24.Is 35461 divisible by 15?
  25. 25.Is 7709 divisible by 8?
  26. 26.Is 39446 divisible by 11?
  27. 27.Is 24596 divisible by 18?
  28. 28.Is 17013 divisible by 8?
  29. 29.Is 9543 divisible by 30?
  30. 30.Is 19100 divisible by 4?
  31. 31.Is 16315 divisible by 5?
  32. 32.Is 8148 divisible by 12?
  33. 33.Is 36887 divisible by 9?
  34. 34.Is 8895 divisible by 4?
  35. 35.Is 59742 divisible by 19?
  36. 36.Is 20238 divisible by 24?
  37. 37.Is 3827 divisible by 3?
  38. 38.Is 8977 divisible by 7?
  39. 39.Is 15948 divisible by 6?
  40. 40.Is 118682 divisible by 18?

Answer key

  1. yes
  2. no
  3. yes
  4. no
  5. yes
  6. yes
  7. yes
  8. no
  9. no
  10. no
  11. no
  12. no
  13. no
  14. no
  15. no
  16. no
  17. yes
  18. no
  19. no
  20. no
  21. yes
  22. no
  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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