Is there any neat way to solve how many digits the number $20!$ have? I'm looking a solution which does not use computers, calculators nor log tables, just pen and paper.
2026-04-09 07:52:10.1775721130
Factorial number of digits
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1
As a rough approximation, multiplying an $n$-digit number by an $m$-digit number yields a result with about $n+m$ digits. So the numbers from 2 to 9 are all 1-digit numbers. From 10 to 20 are all 2-digit numbers. That suggests we should have about 18 digits or so.
Wolfram|Alpha claims that $20! = 2.4 \times 10^{18}$. Not far off! :-D