How to write $c$ when $c\mid pa$?

Question

If $p$ is a prime number and $\gcd(p,a)=1$ for some natural number $a$. We also have $c\mid (p\cdot a)$ Can we say that $c=p\cdot d$ for some divisor $d$ of $a$?

Answer 1

No. Take $a$ coprime with $p$ and $c$ a divisor of $a$.