Synthetic aperture interferometric radiometer (SAIR), as a passive and high-sensitivity receiver, often encounters the pollution issue of radio frequency interference (RFI) sources. An effective method is to get the geolocalization of RFI sources and disable them by the government or other civilizations. Therefore, RFI geolocalization is a crucial step for RFI mitigation. Previous works based on matrix completion (MC) show improved spatial resolution for RFI geolocalization. However, the singular value decomposition (SVD) of the MC is time-consuming. In this study, we propose a fast RFI localization method based on the reweighted matrix factorization (RMF) to improve computation efficiency. First, we establish a robust MC model by leveraging the low-rank property of the RFI-contained covariance matrix. Then, we reformulate the MC model as an RMF model by introducing matrix factorization. Third, the alternating direction method of multipliers (ADMMs) is used to solve the RMF model. Finally, the multiple signal classification (MUSIC) algorithm locates RFI sources. Results obtained using Soil Moisture and Ocean Salinity (SMOS) satellite data demonstrate the effectiveness of the proposed method in computation efficiency.