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Nice one. Using the standard ieee 754 double precision floating point format, we can exactly represent integers less than $2^{53}$, multiplied by a power of 2. When we try to find the largest n where n! can be represented that way, then for example the factor 12 of 12! equals $3 \cdot 2^2$. If my calculator gets it right then the largest n is 22, with $22! ≈ ...

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