We here provide a distribution-free approach to the random factor analysis model. We show that it leads to the same estimating equations as for the classical ML estimates under normality, but more easily derived, and valid also in the case of more variables than observations ($p>n$). For this case we also advocate a simple iteration method. In an illustration with $p=2000$ and $n=22$ it was seen to lead to convergence after just a few iterations. We show that there is no reason to expect Heywood cases to appear, and that the factor scores will typically be precisely estimated/predicted as soon as $p$ is large. We state as a general conjecture that the nice behaviour is not despite $p>n$, but because $p>n$.