A synthetic aperture radar (SAR) system is severely affected by radio frequency systems, such as TV and cellular networks. Previous studies showed that narrowband radio frequency interference (RFI) is low rank and used the nuclear norm as a low-rank regularization to extract the RFI from the received signal. However, the nuclear norm is not an appropriate approximation of the true rank function. Hence, in this paper, the reweighted matrix-factorization (RMF) algorithm and the matrix-factorization decomposition (MFD) algorithm are proposed to suppress narrowband RFI for SAR systems, where the RMF algorithm uses the reweighted scheme to approximate the rank function, while the MFD algorithm restrains the upper bound of the rank as a prior condition. Moreover, the introduction of the MF scheme dramatically decreases the computational complexity and efficiently suppresses RFI. In addition, we further show that the sparse regularization of the useful signal (i.e., the useful SAR echo) not only protects the strong scatterers of the useful signal but also avoids low-rank overfitting. We employ the real SAR signals of both the sparse scene and the nonsparse scene with the measured RFI to verify the effectiveness of the proposed methods, and the proposed methods outperform the other methods for RFI suppression.