Largest Factorial Represented Exactly In Floating Point System

"Find the largest integer such that 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.

Re: Largest Factorial Represented Exactly In Floating Point System

Quote:

Originally Posted by

**mathematicalbagpiper** "Find the largest integer

such that

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

Of these are zeros.

So you now need and

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

CB