This paper is concerned with the applications of discrete Fourier transforms in identification of the number of common factors of static approximate factor models. We report and explain the effects of discrete Fourier transforms to matrices, and show how the effects can be used to improve the performance of a number of eigenvalue-based estimators. In addition, we develop a set of pseudo-eigenvalues\ using cross-sectional discrete Fourier transforms, and use them to develop new estimators. Mathematical proofs of the consistency of the new estimators are provided, and Monte Carlo experiments are conducted to compare the new estimators with some existing ones in the literature.