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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 504 · 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 5933 divisible by 17?
  2. 2.Is 3803 divisible by 2?
  3. 3.Is 1974 divisible by 6?
  4. 4.Is 72903 divisible by 17?
  5. 5.Is 121348 divisible by 23?
  6. 6.Is 11708 divisible by 3?
  7. 7.Is 3849 divisible by 29?
  8. 8.Is 17161 divisible by 3?
  9. 9.Is 6960 divisible by 7?
  10. 10.Is 26150 divisible by 4?
  11. 11.Is 1436 divisible by 23?
  12. 12.Is 45268 divisible by 15?
  13. 13.Is 86119 divisible by 15?
  14. 14.Is 89160 divisible by 30?
  15. 15.Is 42707 divisible by 10?
  16. 16.Is 21295 divisible by 7?
  17. 17.Is 109672 divisible by 19?
  18. 18.Is 35972 divisible by 8?
  19. 19.Is 52078 divisible by 10?
  20. 20.Is 11557 divisible by 3?
  21. 21.Is 18519 divisible by 8?
  22. 22.Is 126904 divisible by 29?
  23. 23.Is 122904 divisible by 18?
  24. 24.Is 6439 divisible by 23?
  25. 25.Is 38956 divisible by 24?
  26. 26.Is 172 divisible by 2?
  27. 27.Is 30457 divisible by 24?
  28. 28.Is 5627 divisible by 3?
  29. 29.Is 9512 divisible by 2?
  30. 30.Is 5508 divisible by 4?
  31. 31.Is 6571 divisible by 5?
  32. 32.Is 13116 divisible by 8?
  33. 33.Is 46768 divisible by 8?
  34. 34.Is 34545 divisible by 5?
  35. 35.Is 89024 divisible by 24?
  36. 36.Is 16110 divisible by 24?
  37. 37.Is 12234 divisible by 3?
  38. 38.Is 7100 divisible by 20?
  39. 39.Is 34657 divisible by 29?
  40. 40.Is 27306 divisible by 6?

Answer key

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

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