The sum of the two smallest positive divisors of an integer $N$ is $6$, while the sum of the two largest positive divisors of $N$ is $1122$. Find $N$.
I came across this question in a Math Olympiad Competition. I am able to find out that the two smallest positive divisors would be $1$ and $5$ but after that, I am not sure how to work on to find out the value of $N$. Can anyone help? Thanks.