A direct factor $A \le G$ is a subgroup for which there exists some $B \le G$ such that $G = A \times B$. If $G = N_1 \times \ldots \times N_k$ and $K \le G$ is a simple subgroup and a direct factor, then $K \cong N_j$ for some $i = 1,\ldots, k$. This could be seen by the Jordan-Hölder theorem, as the $N_i$ are the composition factors in some series, and the simple direct factors also.
Do you know an example for a simple and normal subgroup $K \le G$, but such that $K$ is not isomorphic to any $N_j$ (and hence $K$ could not be a direct factor)? As shown above the condition that it is a direct factor is sufficent, but is it also necessary?