What is the biggest factorial number

There is no "biggest" factorial number in a mathematical sense—factorials extend infinitely since you can always compute (n+1)! for any given n. However, practical computational limits exist: 170! is often cited as the largest factorial exactly representable in standard double-precision floating-point format before the result exceeds representable values and returns infinity in most programming environments.

Using arbitrary-precision arithmetic, mathematicians have computed factorials with millions of digits—100,000! contains over 450,000 digits, and calculations extending to 1,000,000! and beyond have been performed for research purposes in computational mathematics. The practical limiting factor isn't whether a factorial can theoretically be calculated but whether computing and storing the result serves any purpose: storage requirements grow exponentially, computation time increases dramatically with each step, and most applications requiring large factorials instead use Stirling's approximation (n! ≈ √(2πn) × (n/e)^n) or work with logarithms of factorials to avoid the computational burden. In fields like cryptography, statistical mechanics, and combinatorics, researchers work with factorials in the thousands or higher, but calculations typically involve ratios, logarithmic forms, or approximations rather than computing complete decimal expansions. The "biggest" factorial ultimately depends on computational resources dedicated to the task and whether the result has any meaningful application beyond demonstrating computational capability.