Let $A$ be a ring, $M_1,\ldots,M_n$ be A-modules and $N_j$ be an $A$-submodule of $M_j$ for $1 \leq j \leq n$
Prove that $$(M_1 \times M_2 \times \cdots \times M_n)/(N_1 \times N_2 \times \cdots \times N_n) \cong (M_1/N_1) \times (M_2/N_2)\times\cdots\times (M_n/N_n)$$
I'm completely lost with this. All I can think of being relevant is the First Isomorphism Theorem and the definition of a submodule.
Would it have something to do with dividing basis elements?