Factorial Length‎

Question

I want to know:For Example:how many digits 10! is without calculate it I need a formula to count for any Integer.Is there formula to calculate the digits of any Integer number?

Answer 1

Working in the decimal system you need to take the logarithm with base $10$, round down and add 1.

For $10!$ the number of digits is therefore $\left \lfloor \log_{10} (10!) \right \rfloor + 1$.