\(312|2\\156|2\\.\ 78|2\\.\ 39|3\\.\ 13|13\\.\ \ 1|\\312=\fbox2\cdot\fbox2\cdot2\cdot\fbox3\cdot13\)
\(444|2\\222|2\\111|3\\.\ 37|37\\.\ \ \ 1|\\444=\fbox2\cdot\fbox2\cdot\fbox3\cdot37\\\\Therefore\ GCF(312;\ 444)=\fbox2\cdot\fbox2\cdot\fbox3=\boxed{\boxed{12}}\)
