$\tau( n!(n+1) ) = 2\times\tau(n!)$. Then what is $n!\;\text{mod} \; (n+1)?$

Question

If the number of factor of $(n+1)!$ is double than the number of factor of $n!$, then find the reminder if $n!$ is divided by $(n+1)$?

I'm not sure if the question mean factor = divisor. However in both cases I cant find a way to start.
Source: BdMO 2015 Noril regional Higher Secondary Question no. 10.