isomorphism, integers of mod $n$. Hello I think this is true, but I'm not sure.

Setup:
If $n = p_{1}\cdot p_{2} \cdots p_{n}$ where $p_{i}$ prime for all $i\in\lbrace 1,\dots,n\rbrace$.
Define the ring $A = p_{j}\mathbb{Z}/n\mathbb{Z}$.

Question:
Is $A$ isomorphic to $\mathbb{Z}/(n/p_{j})\mathbb{Z}$? And why?

Hint: Does $\mathbb Z/(n/p_i)\mathbb Z$ have a multiplicative unit? Does $p_i\mathbb Z/n\mathbb Z$?
