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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 383 · 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 45164 divisible by 18?
  2. 2.Is 19041 divisible by 3?
  3. 3.Is 40825 divisible by 19?
  4. 4.Is 126869 divisible by 23?
  5. 5.Is 23705 divisible by 9?
  6. 6.Is 127853 divisible by 24?
  7. 7.Is 4723 divisible by 10?
  8. 8.Is 140448 divisible by 23?
  9. 9.Is 3405 divisible by 3?
  10. 10.Is 7930 divisible by 5?
  11. 11.Is 16936 divisible by 8?
  12. 12.Is 586 divisible by 3?
  13. 13.Is 3249 divisible by 15?
  14. 14.Is 352 divisible by 3?
  15. 15.Is 49413 divisible by 13?
  16. 16.Is 11353 divisible by 29?
  17. 17.Is 80838 divisible by 19?
  18. 18.Is 32665 divisible by 24?
  19. 19.Is 2684 divisible by 11?
  20. 20.Is 9028 divisible by 24?
  21. 21.Is 3528 divisible by 18?
  22. 22.Is 166230 divisible by 30?
  23. 23.Is 24890 divisible by 4?
  24. 24.Is 15750 divisible by 15?
  25. 25.Is 15486 divisible by 17?
  26. 26.Is 29899 divisible by 9?
  27. 27.Is 3097 divisible by 19?
  28. 28.Is 17851 divisible by 5?
  29. 29.Is 24520 divisible by 10?
  30. 30.Is 13460 divisible by 20?
  31. 31.Is 78580 divisible by 20?
  32. 32.Is 3837 divisible by 7?
  33. 33.Is 74904 divisible by 12?
  34. 34.Is 45619 divisible by 7?
  35. 35.Is 2520 divisible by 30?
  36. 36.Is 7641 divisible by 9?
  37. 37.Is 128557 divisible by 23?
  38. 38.Is 60161 divisible by 9?
  39. 39.Is 3480 divisible by 24?
  40. 40.Is 1527 divisible by 3?

Answer key

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

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