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The greatest common divisor of two positive integers $a$ and $b$ is the largest positive integer that divides both $a$ and $b$ (written $\gcd(a, b)$). For example, $\gcd(4, 6) = 2$ and $\gcd(5, 6) = 1.$
$(a)$ Prove that $\gcd(a, b) = \gcd(a, b − a).$
$(b)$ Let $r\equiv b (\mod a)$. Using part $(a)$, prove that $\gcd(a, b) = \gcd(a, r)$.
Can someone help me explain how to do this question $?$