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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 558 · 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 46719 divisible by 29?
  2. 2.Is 43959 divisible by 17?
  3. 3.Is 21348 divisible by 9?
  4. 4.Is 20160 divisible by 3?
  5. 5.Is 22920 divisible by 8?
  6. 6.Is 63618 divisible by 12?
  7. 7.Is 39176 divisible by 7?
  8. 8.Is 17820 divisible by 9?
  9. 9.Is 1046 divisible by 3?
  10. 10.Is 25216 divisible by 6?
  11. 11.Is 30958 divisible by 6?
  12. 12.Is 106823 divisible by 30?
  13. 13.Is 8736 divisible by 5?
  14. 14.Is 4613 divisible by 7?
  15. 15.Is 37653 divisible by 11?
  16. 16.Is 33414 divisible by 10?
  17. 17.Is 130982 divisible by 20?
  18. 18.Is 60584 divisible by 9?
  19. 19.Is 34961 divisible by 18?
  20. 20.Is 15975 divisible by 5?
  21. 21.Is 18142 divisible by 5?
  22. 22.Is 10110 divisible by 30?
  23. 23.Is 64680 divisible by 30?
  24. 24.Is 53371 divisible by 15?
  25. 25.Is 3840 divisible by 2?
  26. 26.Is 9648 divisible by 15?
  27. 27.Is 20933 divisible by 3?
  28. 28.Is 111741 divisible by 19?
  29. 29.Is 15261 divisible by 5?
  30. 30.Is 4775 divisible by 2?
  31. 31.Is 75569 divisible by 24?
  32. 32.Is 136490 divisible by 20?
  33. 33.Is 89317 divisible by 30?
  34. 34.Is 63908 divisible by 13?
  35. 35.Is 6520 divisible by 10?
  36. 36.Is 3623 divisible by 4?
  37. 37.Is 51534 divisible by 9?
  38. 38.Is 98287 divisible by 19?
  39. 39.Is 165300 divisible by 29?
  40. 40.Is 72849 divisible by 24?

Answer key

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

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