On factoriality of nodal threefolds

We prove the $\mathbb{Q}$-factoriality of a nodal hypersurface in ${\mathbb{P}}^4$ of degree $n$ with at most $\frac{(n-1{)}^2}{4}$ nodes and the $\mathbb{Q}$-factoriality of a double cover of ${\mathbb{P}}^3$ branched over a nodal surface of degree $2r$ with at most $\frac{(2r-1)r}{3}$ nodes.