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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 781 · 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 15106 divisible by 7?
  2. 2.Is 30787 divisible by 13?
  3. 3.Is 31666 divisible by 6?
  4. 4.Is 30714 divisible by 19?
  5. 5.Is 58036 divisible by 30?
  6. 6.Is 123615 divisible by 24?
  7. 7.Is 49621 divisible by 11?
  8. 8.Is 26384 divisible by 4?
  9. 9.Is 21949 divisible by 20?
  10. 10.Is 142 divisible by 8?
  11. 11.Is 20760 divisible by 3?
  12. 12.Is 99203 divisible by 18?
  13. 13.Is 18101 divisible by 19?
  14. 14.Is 7197 divisible by 2?
  15. 15.Is 113693 divisible by 29?
  16. 16.Is 42255 divisible by 15?
  17. 17.Is 10503 divisible by 11?
  18. 18.Is 17081 divisible by 5?
  19. 19.Is 163003 divisible by 29?
  20. 20.Is 3338 divisible by 15?
  21. 21.Is 3589 divisible by 2?
  22. 22.Is 48079 divisible by 15?
  23. 23.Is 23597 divisible by 7?
  24. 24.Is 41430 divisible by 15?
  25. 25.Is 127940 divisible by 20?
  26. 26.Is 24053 divisible by 12?
  27. 27.Is 71542 divisible by 19?
  28. 28.Is 103252 divisible by 20?
  29. 29.Is 53778 divisible by 11?
  30. 30.Is 58440 divisible by 15?
  31. 31.Is 4032 divisible by 5?
  32. 32.Is 48042 divisible by 9?
  33. 33.Is 9521 divisible by 7?
  34. 34.Is 12281 divisible by 9?
  35. 35.Is 46615 divisible by 18?
  36. 36.Is 9387 divisible by 2?
  37. 37.Is 31943 divisible by 5?
  38. 38.Is 79441 divisible by 20?
  39. 39.Is 17931 divisible by 10?
  40. 40.Is 7208 divisible by 3?

Answer key

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

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