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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 512 · 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 39451 divisible by 7?
  2. 2.Is 19320 divisible by 5?
  3. 3.Is 108555 divisible by 30?
  4. 4.Is 105094 divisible by 17?
  5. 5.Is 41910 divisible by 15?
  6. 6.Is 4483 divisible by 6?
  7. 7.Is 23550 divisible by 4?
  8. 8.Is 25713 divisible by 8?
  9. 9.Is 78356 divisible by 18?
  10. 10.Is 7824 divisible by 4?
  11. 11.Is 52888 divisible by 10?
  12. 12.Is 79486 divisible by 24?
  13. 13.Is 47952 divisible by 9?
  14. 14.Is 48259 divisible by 7?
  15. 15.Is 48184 divisible by 8?
  16. 16.Is 35283 divisible by 7?
  17. 17.Is 81374 divisible by 23?
  18. 18.Is 53944 divisible by 11?
  19. 19.Is 43008 divisible by 7?
  20. 20.Is 7016 divisible by 10?
  21. 21.Is 155820 divisible by 30?
  22. 22.Is 730 divisible by 10?
  23. 23.Is 399 divisible by 6?
  24. 24.Is 12064 divisible by 8?
  25. 25.Is 37782 divisible by 9?
  26. 26.Is 17853 divisible by 4?
  27. 27.Is 97150 divisible by 19?
  28. 28.Is 45330 divisible by 9?
  29. 29.Is 4349 divisible by 2?
  30. 30.Is 6479 divisible by 2?
  31. 31.Is 129618 divisible by 19?
  32. 32.Is 3094 divisible by 2?
  33. 33.Is 5025 divisible by 4?
  34. 34.Is 8928 divisible by 24?
  35. 35.Is 34905 divisible by 15?
  36. 36.Is 20730 divisible by 4?
  37. 37.Is 15961 divisible by 11?
  38. 38.Is 24773 divisible by 6?
  39. 39.Is 49913 divisible by 10?
  40. 40.Is 23972 divisible by 4?

Answer key

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

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