A semigroup \(S\) is called factorizable if \(S=GE=EG\) where \(G\) is a subgroup of \(S\) and \(E\) is its set of idempotents; \(S\) is locally factorizable if \(eSe\) is factorizable for every idempotent \(e\). Suppose \(S\) is a subsemigroup of the partial transformation semigroup \(P(X)\) with identity \(\varepsilon\). We say that \(S\) is \(\varepsilon\)-complete if \(\alpha\in P(X)\) and \(\alpha{\mathcal R}\varepsilon\) in \(P(X)\) and \(\alpha\varepsilon=\alpha\) together imply that \(\alpha\in S\). It is proved that \(S\) is then factorizable if and only if the rank of \(\varepsilon\) is finite. As corollaries we see that the ideal of \(P(X)\) of mappings less than a given finite rank and the subsemigroup of \(P(X)\) of mappings of finite shift are factorizable. The final section has as its subject \(L(V)\), the subsemigroup under composition of all linear transformations of a vector space \(V\) into itself. Results on factorizability and local factorizability are discussed: for example, \(L(V)\) is factorizable if and only if \(V\) is of finite dimension.