Factoriality and Néron-Severi groups

Let X  be a projective variety with isolated singularities, complete intersection of a smooth hypersurface G of degree k, with a smooth hypersurface F of degree n>k. Denote by NS_m(F) and NS_m(X) the m-th Néron-Severi groups. We prove that if rkNS_m(F)=1 then rkNS_m(X)=1. Moreover we prove that if F is general  containing X and n>max{k,2m+1}, then the natural map from NS_m(X)_Q (the Néron-Severi group tensored by the rationals) to NS_m(F)_Q is surjective. When X is a threefold we deduce that X is factorial if and only if rkNS_2(F)=1. This allows us to prove the existence of factorial threefolds with many singularities.