This article proposes a procedure to estimate the number of common factors <i>k</i> in a static approximate factor model. The building block of the analysis is the fact that the first <i>k</i> eigenvalues of the covariance matrix of the data diverge, while the others stay bounded. On the grounds of this, we propose a test for the null that the <i>i</i>th eigenvalue diverges, using a randomized test statistic based directly on the estimated eigenvalue. The test only requires minimal assumptions on the data, and no …