jmc

The prime factorization of $200$ is $2^3\cdot 5^2$. It follows that $N=(1+2+2^2+2^3)(1+5+5^2)$, as each factor of $200$ is represented when the product is expanded. It follows that $N=(1+2+4+8)(1+5+25)=(15)(31)$. The largest prime factor is $\boxed{31}$.