Question

Let a >= b.
show that gcd(a,b) = gcd(a-b, b) ​

Answer 1

let
`\gcd(a,b)= G` , $a\ge b$

$\therefore a=G\cdot m$ and $b=G\cdot n$

$a-b=Gm-Gn=G(m-n)$

Now, $\gcd(a-b,b)$ clearly is, $G$