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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 350 · 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 66638 divisible by 11?
  2. 2.Is 8239 divisible by 7?
  3. 3.Is 52445 divisible by 17?
  4. 4.Is 122930 divisible by 19?
  5. 5.Is 32802 divisible by 11?
  6. 6.Is 49578 divisible by 9?
  7. 7.Is 134108 divisible by 20?
  8. 8.Is 21955 divisible by 4?
  9. 9.Is 14658 divisible by 7?
  10. 10.Is 3492 divisible by 3?
  11. 11.Is 466 divisible by 2?
  12. 12.Is 10098 divisible by 6?
  13. 13.Is 10746 divisible by 2?
  14. 14.Is 70941 divisible by 17?
  15. 15.Is 50640 divisible by 30?
  16. 16.Is 80599 divisible by 12?
  17. 17.Is 61394 divisible by 19?
  18. 18.Is 27886 divisible by 5?
  19. 19.Is 2337 divisible by 15?
  20. 20.Is 9200 divisible by 8?
  21. 21.Is 15040 divisible by 7?
  22. 22.Is 8127 divisible by 9?
  23. 23.Is 39652 divisible by 23?
  24. 24.Is 56666 divisible by 29?
  25. 25.Is 93636 divisible by 18?
  26. 26.Is 125052 divisible by 19?
  27. 27.Is 6307 divisible by 18?
  28. 28.Is 32331 divisible by 7?
  29. 29.Is 40249 divisible by 15?
  30. 30.Is 1185 divisible by 5?
  31. 31.Is 31224 divisible by 5?
  32. 32.Is 35953 divisible by 8?
  33. 33.Is 64975 divisible by 23?
  34. 34.Is 56597 divisible by 24?
  35. 35.Is 17354 divisible by 3?
  36. 36.Is 14094 divisible by 3?
  37. 37.Is 87195 divisible by 15?
  38. 38.Is 37990 divisible by 29?
  39. 39.Is 30055 divisible by 30?
  40. 40.Is 121704 divisible by 23?

Answer key

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

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