Let $X\subset\mathbb{P} _{\mathbb{C}}^N$ be a normal complete intersection.
$X$ is called factorial if every Weil divisor on it is Cartier; equivalently if all local rings $\mathcal{O}_{X,x}$ are unique factorization domains.
Is it true that if $$ \dim(\mathrm{sing}(X))<\dim(X)-3, $$ then $X$ is factorial?
Thanks.
