In this paper, a general definition of factorization of meromorphic functions of several variables is given. We have proved a general Malmquist type theorem of partial differential equations and prove the pseudo-prime ness of meromorphic solutions of system of Riccati partial differential equations with polynomial coefficients. Also it is proved that any finite order meromorphic solution of linear partial differential equations with rational coefficients must be pseudo-prime. The main tool used in the paper is Nevanlinna type of higher-dimensional value distribution theory.