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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 617 · 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 22204 divisible by 13?
  2. 2.Is 66196 divisible by 19?
  3. 3.Is 23625 divisible by 7?
  4. 4.Is 21818 divisible by 4?
  5. 5.Is 134993 divisible by 24?
  6. 6.Is 87088 divisible by 19?
  7. 7.Is 12672 divisible by 5?
  8. 8.Is 21205 divisible by 8?
  9. 9.Is 11086 divisible by 4?
  10. 10.Is 11414 divisible by 10?
  11. 11.Is 31410 divisible by 6?
  12. 12.Is 14996 divisible by 23?
  13. 13.Is 65407 divisible by 13?
  14. 14.Is 75642 divisible by 12?
  15. 15.Is 65835 divisible by 11?
  16. 16.Is 44206 divisible by 23?
  17. 17.Is 28994 divisible by 19?
  18. 18.Is 84434 divisible by 24?
  19. 19.Is 17031 divisible by 29?
  20. 20.Is 42510 divisible by 18?
  21. 21.Is 32929 divisible by 18?
  22. 22.Is 10934 divisible by 11?
  23. 23.Is 79728 divisible by 12?
  24. 24.Is 81026 divisible by 13?
  25. 25.Is 121820 divisible by 23?
  26. 26.Is 15551 divisible by 5?
  27. 27.Is 31453 divisible by 18?
  28. 28.Is 27015 divisible by 20?
  29. 29.Is 2726 divisible by 4?
  30. 30.Is 18921 divisible by 3?
  31. 31.Is 39540 divisible by 10?
  32. 32.Is 44415 divisible by 19?
  33. 33.Is 92735 divisible by 17?
  34. 34.Is 43899 divisible by 10?
  35. 35.Is 23208 divisible by 12?
  36. 36.Is 53041 divisible by 17?
  37. 37.Is 30758 divisible by 15?
  38. 38.Is 1328 divisible by 11?
  39. 39.Is 52338 divisible by 11?
  40. 40.Is 31453 divisible by 7?

Answer key

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

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