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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 686 · 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 6426 divisible by 7?
  2. 2.Is 24522 divisible by 6?
  3. 3.Is 2380 divisible by 10?
  4. 4.Is 132269 divisible by 23?
  5. 5.Is 67860 divisible by 15?
  6. 6.Is 17812 divisible by 4?
  7. 7.Is 10769 divisible by 6?
  8. 8.Is 80155 divisible by 23?
  9. 9.Is 103184 divisible by 18?
  10. 10.Is 7970 divisible by 6?
  11. 11.Is 71774 divisible by 17?
  12. 12.Is 13419 divisible by 9?
  13. 13.Is 68356 divisible by 18?
  14. 14.Is 42210 divisible by 7?
  15. 15.Is 45912 divisible by 12?
  16. 16.Is 2491 divisible by 3?
  17. 17.Is 706 divisible by 4?
  18. 18.Is 4360 divisible by 5?
  19. 19.Is 54791 divisible by 17?
  20. 20.Is 51186 divisible by 17?
  21. 21.Is 131747 divisible by 29?
  22. 22.Is 150626 divisible by 29?
  23. 23.Is 1007 divisible by 19?
  24. 24.Is 18841 divisible by 10?
  25. 25.Is 21268 divisible by 7?
  26. 26.Is 6534 divisible by 3?
  27. 27.Is 17590 divisible by 4?
  28. 28.Is 13198 divisible by 11?
  29. 29.Is 9684 divisible by 2?
  30. 30.Is 16002 divisible by 9?
  31. 31.Is 63176 divisible by 17?
  32. 32.Is 5632 divisible by 19?
  33. 33.Is 238 divisible by 3?
  34. 34.Is 9592 divisible by 5?
  35. 35.Is 115302 divisible by 18?
  36. 36.Is 23114 divisible by 7?
  37. 37.Is 54651 divisible by 11?
  38. 38.Is 32497 divisible by 8?
  39. 39.Is 165511 divisible by 29?
  40. 40.Is 26167 divisible by 6?

Answer key

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

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