Fix a separable infinite-dimensional Hilbert space \(H\) and for each positive integer \(n\), write \(\overline{{\mathcal P}_n}\) for the norm closure of the set of operators on \(H\) that can be expressed as the product of \(n\) positive invertible operators. The author characterizes \(\overline{{\mathcal P}_2}\) as a special set of biquasitriangular operators, shows that every operator whose essential spectrum contains zero belongs to \(\overline{{\mathcal P}_3}\) and proves that \(\overline{{\mathcal P}_4}=\overline{{\mathcal P}_5}\).