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Answer is C, 25. 75 doesn't go into 100 or 175 evenly, so that wouldn't work, 20 only goes into 100 evenly, and 5 goes into all of them, but it's not the greatest common factor. 25 works for all 3, and it is the greatest number that works, so it is the greatest common factor, or GCF. So it has to be C, 25.
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[tex]75|5\\15|5\\.\ 3|3\\.\ 1|\\75=\boxed{5}\cdot\boxed{5}\cdot3\\\\100|5\\.\ 20|5\\.\ \ 4|2\\.\ \ 2|2\\.\ \ 1|\\100=\boxed{5}\cdot\boxed{5}\cdot2\cdot2\\\\175|5\\.\ 35|5\\.\ \ 7|7\\.\ \ 1|\\175=\boxed{5}\cdot\boxed{5}\cdot7\\\\GCF(75;\ 100;\ 175)=\boxed{5}\cdot\boxed{5}=25[/tex]

Answer: 25

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