Challenge Level

For a positive integer $n$, we define $n!$ to be the product of all the positive integers from $1$ to $n$; that is $n!=1\times 2\times 3\times\ldots\times n$.

If $n!=2^{15}\times 3^6\times 5^3\times 7^2\times 11\times 13$, what is the value of $n$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.