This paper introduces a factor-solve method that efficiently computes Thévenin equivalents for all buses in the power system. A range of real-time stability assessment methods relies on Thévenin equivalents, and it is therefore essential that these methods can be determined fast and efficiently. The factor-solve method has runtime for computing Thévenin voltage that scales linearly with system size resulting in runtime of only a few milliseconds even for systems with several thousand buses. The computations only need the sparse admittance matrix for the power system and a sparse factorization resulting in low memory requirements, and furthermore, Thévenin impedances can be determined in parallel. The factor-solve method is compared to a reference method that uses coefficients for super-position to determine the Thévenin equivalents. The reference method is shown to have unsatisfactory runtime and complexity. The factor-solve method is tested, parallelized, and analyzed, which shows a considerable speedup in computations of Thévenin equivalents enabling them to be computed in real time.