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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 640 · 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 5346 divisible by 10?
  2. 2.Is 13356 divisible by 7?
  3. 3.Is 38997 divisible by 7?
  4. 4.Is 4992 divisible by 8?
  5. 5.Is 34059 divisible by 18?
  6. 6.Is 99893 divisible by 19?
  7. 7.Is 27012 divisible by 6?
  8. 8.Is 65857 divisible by 29?
  9. 9.Is 6020 divisible by 10?
  10. 10.Is 11475 divisible by 29?
  11. 11.Is 102168 divisible by 18?
  12. 12.Is 118232 divisible by 20?
  13. 13.Is 58697 divisible by 29?
  14. 14.Is 154363 divisible by 23?
  15. 15.Is 9740 divisible by 2?
  16. 16.Is 52411 divisible by 11?
  17. 17.Is 28863 divisible by 9?
  18. 18.Is 52906 divisible by 8?
  19. 19.Is 3310 divisible by 10?
  20. 20.Is 10509 divisible by 6?
  21. 21.Is 10830 divisible by 19?
  22. 22.Is 51724 divisible by 23?
  23. 23.Is 36913 divisible by 7?
  24. 24.Is 99698 divisible by 15?
  25. 25.Is 7296 divisible by 6?
  26. 26.Is 47503 divisible by 23?
  27. 27.Is 16160 divisible by 6?
  28. 28.Is 36060 divisible by 20?
  29. 29.Is 10788 divisible by 29?
  30. 30.Is 3115 divisible by 5?
  31. 31.Is 91010 divisible by 19?
  32. 32.Is 16949 divisible by 17?
  33. 33.Is 2297 divisible by 30?
  34. 34.Is 9588 divisible by 2?
  35. 35.Is 10020 divisible by 6?
  36. 36.Is 30379 divisible by 29?
  37. 37.Is 3192 divisible by 17?
  38. 38.Is 10572 divisible by 17?
  39. 39.Is 4256 divisible by 8?
  40. 40.Is 103980 divisible by 20?

Answer key

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

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