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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 670 · 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 15620 divisible by 8?
  2. 2.Is 42733 divisible by 8?
  3. 3.Is 71726 divisible by 12?
  4. 4.Is 19455 divisible by 5?
  5. 5.Is 78542 divisible by 12?
  6. 6.Is 68264 divisible by 10?
  7. 7.Is 91632 divisible by 23?
  8. 8.Is 23114 divisible by 7?
  9. 9.Is 3904 divisible by 5?
  10. 10.Is 31738 divisible by 7?
  11. 11.Is 767 divisible by 13?
  12. 12.Is 28845 divisible by 15?
  13. 13.Is 72858 divisible by 23?
  14. 14.Is 9563 divisible by 3?
  15. 15.Is 11453 divisible by 13?
  16. 16.Is 194164 divisible by 30?
  17. 17.Is 34831 divisible by 5?
  18. 18.Is 34139 divisible by 7?
  19. 19.Is 86826 divisible by 13?
  20. 20.Is 15660 divisible by 4?
  21. 21.Is 189184 divisible by 29?
  22. 22.Is 132659 divisible by 23?
  23. 23.Is 111710 divisible by 18?
  24. 24.Is 85095 divisible by 24?
  25. 25.Is 40804 divisible by 17?
  26. 26.Is 154019 divisible by 29?
  27. 27.Is 17717 divisible by 7?
  28. 28.Is 19983 divisible by 6?
  29. 29.Is 89218 divisible by 15?
  30. 30.Is 5166 divisible by 9?
  31. 31.Is 79260 divisible by 30?
  32. 32.Is 10800 divisible by 8?
  33. 33.Is 8709 divisible by 2?
  34. 34.Is 507 divisible by 2?
  35. 35.Is 29664 divisible by 9?
  36. 36.Is 57396 divisible by 15?
  37. 37.Is 57415 divisible by 12?
  38. 38.Is 11585 divisible by 7?
  39. 39.Is 7303 divisible by 4?
  40. 40.Is 160402 divisible by 23?

Answer key

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

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