a=su，b=tu，

You can also divide r because r = a-bq = su-qtu = (s-qt) u.

On the contrary, every integer v divisible by b and r has

b=s'v，r=t'v

Can also be divisible by a, because a = bq+r = s' VQ+t' v = (s' q+t') v.

So every common factor of A and B is also the common factor of B and R, and vice versa. In this way, since all common factor sets of A and B are the same as those of B and R, the greatest common factor of A and B must be equal to the greatest common factor of B and R..

In fact, there is a more subtraction technique, which is also a good way to find the greatest common divisor.