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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 287 · 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 55202 divisible by 18?
  2. 2.Is 88914 divisible by 29?
  3. 3.Is 612 divisible by 4?
  4. 4.Is 77928 divisible by 24?
  5. 5.Is 29786 divisible by 7?
  6. 6.Is 1384 divisible by 17?
  7. 7.Is 93600 divisible by 15?
  8. 8.Is 12088 divisible by 9?
  9. 9.Is 10070 divisible by 7?
  10. 10.Is 30745 divisible by 19?
  11. 11.Is 31656 divisible by 12?
  12. 12.Is 28398 divisible by 5?
  13. 13.Is 62816 divisible by 10?
  14. 14.Is 58078 divisible by 9?
  15. 15.Is 40104 divisible by 8?
  16. 16.Is 78925 divisible by 24?
  17. 17.Is 21034 divisible by 11?
  18. 18.Is 9434 divisible by 2?
  19. 19.Is 83971 divisible by 20?
  20. 20.Is 12224 divisible by 2?
  21. 21.Is 80896 divisible by 17?
  22. 22.Is 34520 divisible by 8?
  23. 23.Is 1479 divisible by 2?
  24. 24.Is 60486 divisible by 17?
  25. 25.Is 23994 divisible by 6?
  26. 26.Is 54743 divisible by 10?
  27. 27.Is 36791 divisible by 13?
  28. 28.Is 45481 divisible by 9?
  29. 29.Is 5135 divisible by 5?
  30. 30.Is 52893 divisible by 19?
  31. 31.Is 68556 divisible by 12?
  32. 32.Is 56696 divisible by 10?
  33. 33.Is 19248 divisible by 12?
  34. 34.Is 156629 divisible by 29?
  35. 35.Is 13568 divisible by 8?
  36. 36.Is 120377 divisible by 19?
  37. 37.Is 67894 divisible by 15?
  38. 38.Is 25214 divisible by 5?
  39. 39.Is 41600 divisible by 13?
  40. 40.Is 168 divisible by 4?

Answer key

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

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