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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 54 · 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 145029 divisible by 29?
  2. 2.Is 31267 divisible by 7?
  3. 3.Is 1980 divisible by 6?
  4. 4.Is 15847 divisible by 17?
  5. 5.Is 27641 divisible by 29?
  6. 6.Is 26733 divisible by 6?
  7. 7.Is 55456 divisible by 10?
  8. 8.Is 52235 divisible by 10?
  9. 9.Is 1018 divisible by 7?
  10. 10.Is 28749 divisible by 19?
  11. 11.Is 6199 divisible by 15?
  12. 12.Is 27013 divisible by 7?
  13. 13.Is 40145 divisible by 7?
  14. 14.Is 28767 divisible by 7?
  15. 15.Is 37710 divisible by 6?
  16. 16.Is 1736 divisible by 7?
  17. 17.Is 7636 divisible by 23?
  18. 18.Is 53970 divisible by 15?
  19. 19.Is 49351 divisible by 10?
  20. 20.Is 56882 divisible by 29?
  21. 21.Is 13651 divisible by 5?
  22. 22.Is 94209 divisible by 20?
  23. 23.Is 109860 divisible by 20?
  24. 24.Is 85032 divisible by 18?
  25. 25.Is 11044 divisible by 5?
  26. 26.Is 91799 divisible by 20?
  27. 27.Is 9200 divisible by 2?
  28. 28.Is 69570 divisible by 30?
  29. 29.Is 8001 divisible by 7?
  30. 30.Is 2843 divisible by 7?
  31. 31.Is 96860 divisible by 24?
  32. 32.Is 544 divisible by 11?
  33. 33.Is 42183 divisible by 12?
  34. 34.Is 72107 divisible by 29?
  35. 35.Is 93638 divisible by 19?
  36. 36.Is 26908 divisible by 9?
  37. 37.Is 23988 divisible by 4?
  38. 38.Is 106904 divisible by 23?
  39. 39.Is 18101 divisible by 8?
  40. 40.Is 22120 divisible by 7?

Answer key

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

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