Commutation division, also known as Euclidean algorithm, is an algorithm to find the greatest common factor of two positive integers. It is the oldest known algorithm, which can be traced back to 3000 years ago.

Let two numbers be a and b(a> B), the steps to find the greatest common divisor (a, b) of A and B are as follows: divide A by B to get A ÷ B = q ... r1(0 ≤ r1). If r 1=0, then (a, b) = b; If r 1≠0, then divide b by r 1 to get b ÷ r 1 = q ... r2 (0 ≤ R2). If r2=0, then (a, b) = r/kloc-0. The divisor of the remainder whose last dividend is the dividend is (a, b).

For example: a=25,b= 15, a/b =1...10, b/1... 5,10.