What is the highest factorial calculated

The highest factorial exactly calculated and stored depends on computational context and purpose. Standard 64-bit computing can precisely represent factorials only up to 20! (2,432,902,008,176,640,000) before exceeding standard integer limits, while 170! is often cited as the highest factorial exactly representable in double-precision floating-point format before reaching infinity in most programming languages.

However, using arbitrary-precision arithmetic libraries, mathematicians and computer scientists have calculated factorials into the millions. Factorials beyond several thousand digits become computationally expensive but remain feasible—100,000! contains over 450,000 digits and has been computed, while even larger factorials exceeding 1,000,000! have been calculated for research purposes in computational mathematics. The practical limit isn't whether we can calculate a factorial but whether the result serves any purpose: storage requirements grow exponentially, computation time increases dramatically, and most applications requiring very large factorials instead use Stirling's approximation or logarithmic representations. In cryptography, combinatorics, and statistical mechanics, researchers regularly work with factorials in the thousands, but the calculations typically involve ratios or logarithms rather than computing the full decimal expansion.