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Math Help - Largest Factorial Represented Exactly In Floating Point System

  1. #1
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    Largest Factorial Represented Exactly In Floating Point System

    "Find the largest integer n such that n! can be represented exactly in the floating point number system where the base is 2, the precision is 24, and the exponent ranges from -100 to 100.

    Well, I don't even know where to start. I think it has something to do with expressing factorials as powers of 2, but other than that I haven't a bloody clue.
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  2. #2
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    Re: Largest Factorial Represented Exactly In Floating Point System

    Quote Originally Posted by mathematicalbagpiper View Post
    "Find the largest integer n such that n! can be represented exactly in the floating point number system where the base is 2, the precision is 24, and the exponent ranges from -100 to 100.

    Well, I don't even know where to start. I think it has something to do with expressing factorials as powers of 2, but other than that I haven't a bloody clue.
    Well the number of binary digits is b=\lceil \lg(n!) \rceil

    Of these z=\lfloor n/2 \rfloor + \lfloor n/4 \rfloor + ... + \lfloor n/2^{\lfloor\lg(n)\rfloor} \rfloor are zeros.

    So you now need b-z\le 24 and z \le 100

    Now trial and error should find the answer pretty quickly (it is less than 20)

    CB
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