GoKawiilSimple formula estimates factorial digit counts without a calculator
A math blog post derives a quick approximation for the number of digits in n!, using the formula n·log10(n/e)+2. Applied to 52!, the estimate yields 69 digits versus the actual 68, demonstrating strong accuracy for large factorials. The post also walks through the underlying derivation using the Gamma function and integration by parts.
GoKawiil's interpretation of the reporting above, not reported fact.
This kind of estimation technique is valuable in fields like combinatorics, cryptography, and computer science, where factorials grow astronomically large and exact computation can be impractical. Understanding the Gamma function connection also bridges discrete factorial math with continuous calculus, a foundational link used throughout probability and statistics.
- The formula n·log10(n/e)+2 closely estimates the digit count of n! without needing a calculator.
- Testing on 52! produced 69 digits versus the true value of 68, showing high accuracy.
- The derivation ties factorials to the Gamma function via integration by parts and induction.
Texas Instruments TI-36X Pro calculator — If you love playing with factorials, logarithms, and Gamma function approximations, a solid scientific calculator like the TI-36X Pro makes checking your estimates against real values quick and easy. It handles large factorials, logs, and exponentials natively, perfect for verifying napkin-math like the digit-count formula in this article. A great companion for anyone who enjoys hands-on number crunching alongside the theory.
See Texas Instruments TI-36X Pro calculator on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.Source: eli.thegreenplace.net, 2026-09-15
Published there as: “How Big Are Factorials?”
Read the original report → The summary and analysis above are GoKawiil's own, written from reporting by the source above. Facts and quotes belong to the original publisher.