Question about property of factorial of a number I can easily find out the value of $k=\frac{n!}{m!}$ if the value of m and n is given.recently I have faced problem and that is in the following:

If the value of k is given under the condition $k(1\le k\le 10^9)$ how can I find out the value of n and m.As far I know there will be multiple values of n and m But I need the smallest value of n.
Please someone help me.
If $n&lt;m$ it is rational number. and if $ m&lt;n$ then exist t$\in \Bbb{N}$ such that n=m+t and $K = \frac {n!}{m!} =\frac{(m+t)!}{m!} = \frac{(t+m)(t+m-1)...(t+m-t-1)((t+m-t)!)}{m!}$  if $ k=a_0  $we must decomposition $ a_0$ .
The lower bound of $k$ is $1$.So,lowest possible value of $n=m=1.$.

The upper bound is equal to $10^9$.So maximum value is $n=10^9!$ and $m=[(10^9)-1]!.$