Mini-challenge - accurate factorials

[EdS2]

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A factorial, in decimal, will generally have a number of trailing zeros. For example
7! = 5040
has 4 digits in total, one trailing zero, and so we can say it has 3 significant digits.

So, given a calculator with some number of digits it can display, we might ask what's the largest factorial that will fit? (For example, consider calculators with 8, 10, 12, 14 digit displays, we ask what value of n would give rise to the large displayable n!)

And, given a calculator which has a scientific notation, such that the trailing zeros can be implicit, and needing only to display the significant digits, we can display even larger factorials. How large is the largest n, such that n! is accurately displayed with 8, 10, 12 or 14 significant digits?

Have fun!