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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 194 · 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 67001 divisible by 19?
  2. 2.Is 54753 divisible by 12?
  3. 3.Is 27156 divisible by 6?
  4. 4.Is 40794 divisible by 11?
  5. 5.Is 1425 divisible by 9?
  6. 6.Is 9325 divisible by 7?
  7. 7.Is 13692 divisible by 4?
  8. 8.Is 48951 divisible by 7?
  9. 9.Is 119496 divisible by 24?
  10. 10.Is 3743 divisible by 10?
  11. 11.Is 181320 divisible by 30?
  12. 12.Is 139198 divisible by 29?
  13. 13.Is 30107 divisible by 19?
  14. 14.Is 17957 divisible by 3?
  15. 15.Is 20340 divisible by 30?
  16. 16.Is 45376 divisible by 30?
  17. 17.Is 13631 divisible by 2?
  18. 18.Is 10107 divisible by 2?
  19. 19.Is 1916 divisible by 11?
  20. 20.Is 3268 divisible by 7?
  21. 21.Is 22580 divisible by 4?
  22. 22.Is 57389 divisible by 12?
  23. 23.Is 194 divisible by 3?
  24. 24.Is 17900 divisible by 3?
  25. 25.Is 18101 divisible by 10?
  26. 26.Is 118237 divisible by 19?
  27. 27.Is 50337 divisible by 23?
  28. 28.Is 4667 divisible by 7?
  29. 29.Is 64851 divisible by 24?
  30. 30.Is 35697 divisible by 9?
  31. 31.Is 41136 divisible by 7?
  32. 32.Is 13565 divisible by 10?
  33. 33.Is 73973 divisible by 20?
  34. 34.Is 39137 divisible by 19?
  35. 35.Is 51864 divisible by 8?
  36. 36.Is 28000 divisible by 8?
  37. 37.Is 37289 divisible by 6?
  38. 38.Is 2352 divisible by 6?
  39. 39.Is 17658 divisible by 10?
  40. 40.Is 23712 divisible by 13?

Answer key

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

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