How big are factorials?

This article explains how to estimate the number of digits in a factorial (like 52!) without a calculator, using a simple logarithmic approximation. It then derives this approximation from Stirling's formula, which is itself derived from the Gamma function. The post covers the Gamma function's definition, its recursive property, and its connection to factorials, followed by a step-by-step derivation of Stirling's approximation. It includes a worked example for 52! and discusses the accuracy of the estimate. The content is technical and mathematical, focusing on numerical analysis and approximation techniques relevant to computer science and applied mathematics.