Shefu and Oogway

Oogway and his friend Shefu went to shop to buy sweets, colours and other things for HOLI of worth $N$. Shefu insist to divide the cost. But Oogway puts up a task which is as follows: If Shefu is able to break $N$ into two non-negative numbers say $a$ and $b$ such that - $gcd(a,b) = min(a,b)$ - Absolute difference $|a-b|$ is minimum. Then Shefu can pay $min(a,b)$ cost, rest will be paid by Oogwa