CEMC Banner

Problem of the Week
Problem E
Sixty-Four!

The product \(64 \times 63 \times 62 \times \cdots \times 3 \times 2 \times 1\) can be written as \(64!\) and called "\(64\) factorial".

In general, the product of the positive integers \(1\) to \(m\) is \[m!=m \times (m-1) \times (m-2) \times \cdots \times 3 \times 2 \times 1\]

If \(64!\) is divisible by \(2025^n\), determine the largest positive integer value of \(n\).