Let $A$ be an integral domain. Show that any $f \in A[X]\backslash \{0\}$ can be written as $f=af_0$, where $f_0 \in A[X]$ is primitive.
I know how to prove for the case $A = \mathbb{Z}$ be choosing a as the biggest number which divide all coefficients in f. But this doesn't work for the general A. Can anyone give me a hint? Many thanks