With the help of constructing matrix and applying elementary transfor-mation, this paper gives the simple and useful solution of the following three prob-lems in elementary number theory: greatest common factor and its times sum, in-definite equation, linear congruence expression series. 本文借助构造矩阵和施行初等变换,为初等数论中以下三个问题提供了简便实用的解法:最大公因数及其倍数和、不定方程,一次同余式组。