The greatest common factor of 54 and 72 is:
\(54|2\\27|3\\.\ 9|3\\.\ 3|3\\.\ 1|\\54=\fbox2\cdot\fbox3\cdot\fbox3\cdot3\\\\72|2\\36|2\\18|2\\.\ 9|3\\.\ 3|3\\.\ 1|\\72=\fbox2\cdot2\cdot2\cdot\fbox3\cdot\fbox3\\\\GCF(54;\ 72)=\fbox2\cdot\fbox3\cdot\fbox3=\boxed{\boxed{18}}\)