I am trying to understand greatest common divisor so If a=bt+r for integers t &amp; r then why gcd(a,b)=gcd(b,r).I am unable to understand it.
My problem is how to somehow relate the the gcd and congruence. I know that $(a,b) = ax + by$. I also know that $a \equiv b \pmod n$ means $n\mid a-b$. Any hints?  Thanks!
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