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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 58 · 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 28101 divisible by 29?
  2. 2.Is 84631 divisible by 13?
  3. 3.Is 20865 divisible by 4?
  4. 4.Is 5796 divisible by 4?
  5. 5.Is 119016 divisible by 19?
  6. 6.Is 69766 divisible by 10?
  7. 7.Is 107539 divisible by 18?
  8. 8.Is 1017 divisible by 5?
  9. 9.Is 8629 divisible by 24?
  10. 10.Is 99714 divisible by 19?
  11. 11.Is 2802 divisible by 2?
  12. 12.Is 23840 divisible by 6?
  13. 13.Is 5513 divisible by 4?
  14. 14.Is 62721 divisible by 9?
  15. 15.Is 18395 divisible by 17?
  16. 16.Is 6240 divisible by 24?
  17. 17.Is 2456 divisible by 2?
  18. 18.Is 28665 divisible by 18?
  19. 19.Is 10765 divisible by 20?
  20. 20.Is 1400 divisible by 3?
  21. 21.Is 82215 divisible by 17?
  22. 22.Is 4802 divisible by 2?
  23. 23.Is 124080 divisible by 20?
  24. 24.Is 107080 divisible by 20?
  25. 25.Is 6880 divisible by 6?
  26. 26.Is 36157 divisible by 7?
  27. 27.Is 11895 divisible by 5?
  28. 28.Is 76531 divisible by 29?
  29. 29.Is 1865 divisible by 11?
  30. 30.Is 79458 divisible by 19?
  31. 31.Is 109917 divisible by 23?
  32. 32.Is 19591 divisible by 13?
  33. 33.Is 15370 divisible by 10?
  34. 34.Is 55170 divisible by 10?
  35. 35.Is 78039 divisible by 23?
  36. 36.Is 122840 divisible by 20?
  37. 37.Is 29853 divisible by 7?
  38. 38.Is 29201 divisible by 5?
  39. 39.Is 15093 divisible by 9?
  40. 40.Is 47600 divisible by 8?

Answer key

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

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