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# Finding number of digits in $$n!$$

Hi!

I have encountered a number of questions asking for the number of digits in $$n!$$. If you know varied methods of solving the same, please do share here.

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• No use of Computer Science is allowed.

Note by Swapnil Das
1 year, 1 month ago

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The first two terms of Stirling's approximation to n! are

$$\ln (n!) = n \ln (n) - n$$

So the number of digits in $$n!$$ can be estimated as $$\lfloor n \ln(10) (\ln (n) - 1) \rfloor + 1$$ · 1 year, 1 month ago