# Another fact on factorial

**Number Theory**Level 4

Let \(T(x)\) denote the number of trailing zeros in \(\prod_{n=1}^{x} n!\) for a positive integer \(x\).

Let \(\{x_1,x_2,\cdots,x_p\}\) be the set of all positive integers \(x_i\) which satisfy the equation

\[T(x_i)-x_i+1=0\]

Find \[T\left(\sum_{i=1}^p x_i\right)-\sum_{i=1}^p x_i+1\]