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Zeros in 1000001!
By Anonymous on Thursday, March 25, 1999 - 04:27 pm:

I am a college student and I need some help!

I need to find out what the Factorial of 1000001 (one million one)is. I have been working on this for some time now, but my teacher is not satisfied with my answer. Right now, I have:
1000001! = 8.263934135437012 E + 5565714

My teacher wants me to find out what the whole mantissa is up until the zeroes begin, then find out exactly how many zeroes there are in the answer.

Any help would be greatly appreciated!

By Chris Jefferson (Caj30) on Tuesday, April 13, 1999 - 10:56 am:

Nasty!

I can't see a way of getting the numbers, but I can get the exact number of zeros...

By now you will have probably done prime factorization. The idea is every number can be expressed as several primes multiplied together in ONLY ONE WAY (nearly!)
For example, 12 = 3*2*2. It is also 2*3*2 or 3*2*2*1*1, but that is just being picky!

The exact number of zeros will be the number of factors of 10 in the final answer, or the number of (5*2) in the final answer.

Here is a little example.

6! =6*5*4*3*2*1

=(3*2)*(5)*(2*2)*(3)*(2)*(1)
=(5*2)*3*2*2*2*3*1

so there is ONE factor of ten in this number!
When expanding this, remember that 25 is 5*5, that 125 is 5*5*5, etc..

However, the number to the right of the mantasa will be VERY long indeed. I know someone who actually worked this out, and it took a network of 28 pentiums working for 3 days. Just check you've got the question right..... ;-)

Hope this helps, this is my first try at this, so excuse me if I've messed up.

Chris