Make It One

Chef is given a positive integer $N$ and we have to convert it to $1$ using some operations. $\newline$ In one operation, Chef can do the following: $\newline$ - Choose a [prime number](https://en.wikipedia.org/wiki/Prime_number) $p$ such that $p$ $|$ $N$ $(p$ divides $N)$. - Replace $N$ with $\frac{N}{p}$. However, Chef is also given some *triggers* of the form $(a,b)$ ($a$ is prime). Thus, if