$f$ and $m$ are polynomials over the field $K$. Prove that if $f=pm+r$, $r≠0$, then their hcf is $1$

Question

$f$ and $m$ are polynomials over the field $K$.

$m$ is irreducible.

Prove that if $f=pm+r$ (dividing $f$ by $m$ with the division algorithm over $K$), $r≠0$, then the hcf of $f$ and $m$ is $1$

The author assumed it without giving any proof, and it isn't obvious to me.