R is a PID(principal integral domain), and $pR+aR=cR$ then how can we say $p \in cR$?

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R is a PID(principal integral domain), and $pR+aR=cR$ then how can we say $p \in cR$?

I know that $pr_1+ar_2 = cr_3 \\ c | (pr_1+ar_2) $

then how can we prove that $c|p$