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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 459 · 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 46998 divisible by 9?
  2. 2.Is 34077 divisible by 10?
  3. 3.Is 9775 divisible by 5?
  4. 4.Is 30714 divisible by 6?
  5. 5.Is 3335 divisible by 23?
  6. 6.Is 4451 divisible by 3?
  7. 7.Is 97794 divisible by 29?
  8. 8.Is 8162 divisible by 24?
  9. 9.Is 43018 divisible by 7?
  10. 10.Is 107471 divisible by 17?
  11. 11.Is 14520 divisible by 15?
  12. 12.Is 28086 divisible by 15?
  13. 13.Is 77291 divisible by 30?
  14. 14.Is 19728 divisible by 24?
  15. 15.Is 48504 divisible by 12?
  16. 16.Is 11527 divisible by 4?
  17. 17.Is 33283 divisible by 10?
  18. 18.Is 4344 divisible by 8?
  19. 19.Is 22879 divisible by 11?
  20. 20.Is 58663 divisible by 11?
  21. 21.Is 13272 divisible by 12?
  22. 22.Is 20808 divisible by 8?
  23. 23.Is 5823 divisible by 4?
  24. 24.Is 34855 divisible by 19?
  25. 25.Is 145595 divisible by 29?
  26. 26.Is 71621 divisible by 20?
  27. 27.Is 1456 divisible by 3?
  28. 28.Is 188910 divisible by 30?
  29. 29.Is 12677 divisible by 15?
  30. 30.Is 20906 divisible by 4?
  31. 31.Is 37709 divisible by 30?
  32. 32.Is 94980 divisible by 15?
  33. 33.Is 1898 divisible by 13?
  34. 34.Is 3039 divisible by 3?
  35. 35.Is 32505 divisible by 6?
  36. 36.Is 67666 divisible by 23?
  37. 37.Is 154908 divisible by 30?
  38. 38.Is 81536 divisible by 13?
  39. 39.Is 92747 divisible by 19?
  40. 40.Is 3196 divisible by 24?

Answer key

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

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