Question

Find the number of zeros at the end of (101)!

Answer 1

The question indirectly want us to calculate for what max k 101! is divisible by $5^k$

k=$\lfloor \frac{101}{5}\rfloor +\lfloor \frac{101}{5^2}\rfloor +\lfloor \frac{101}{5^3}\rfloor +....$ where $\lfloor .\rfloor$ denotes Greatest Integer Function

k=20+4=24

So number of zeros at the end of 101!=24