If a and b are positive integers, then you know that a=bq+r, 0\le r<b, where q is a whole number. Prove that…

If $a$ and $b$ are positive integers, then you know that $a=bq+r$, $0\le r<b$, where $q$ is a whole number. Prove that HCF$(a,b)=$ HCF$(b,r)$. [Hint: Let HCF$(b,r)=h$. So $b=k_{1}h$ and $r=k_{2}h$, where $k_1,k_2$ are coprime.]