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Simple formula estimates the digit count of large factorials without a calculator

A math blog post derives a quick approximation for how many digits a factorial like 52! contains, using the formula n·log10(n/e)+2. Applied to 52!, the method predicts 69 digits versus the actual 68, showing strong accuracy for such large numbers. The post then explains the underlying math, connecting factorials to the Gamma function and deriving its recursive property through integration by parts.

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