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Factorial (n) for n > 24 is greater than 10^n.

24! is approximately Avogadro's number (about a 3% difference).

inverse Gamma function of Avogadro's number (6.02 × 10²³) is ~ 24.99056

Sure, but "23.99067408! is Avogadro's number" is both harder to remember and less cool than "24! is almost Avogadro's number".

Sure. I wasn't disagreeing with you; just curious how close the coincidence was.