最大公因数（Greatest Common Divisor，简写为G.C.D.；或Highest Common Factor，简写为H.C.F.），指某几个整数共有因数中最大的一个。

求两个整数最大公因数主要的方法：

两个整数的最大公因数和最小公倍数（L.C.M.）的关系：

两个整数的最大公因数可用于计算两数的最小公倍数，或分数化简成最简分数。

两个整数的最大公因数和最小公倍数中存在分配律：

在座标里，将点（0, 0）和（a, b）连起来，通过整数座标的点的数目（除了（0, 0）一点之外）就是G.C.D.(a, b)。

In mathematics, the greatest common divisor (***) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the *** of 8 and 12 is 4.

The greatest common divisor is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.