Decimal Places in Large FactorialsDate: 04/29/2003 at 18:33:40 From: Teresa Subject: Large factorial numbers Is there an easy way to find how many decimal places or how many zeros the decimal notation of a large factorial number will have? Date: 04/30/2003 at 03:27:02 From: Doctor Roy Subject: Re: Large factorial numbers Hi, Thanks for writing to Dr. Math. There is a formula for finding the number of zeros a factorial number will have. It is: floor(n/5) + floor(n/25) + floor(n/125) + ... + floor(n/5^n) + ... The floor function means round down to the nearest integer. For example, let's take 5!, or n = 5. floor(5/5) = floor(1) = 1. So, 5! ends in 1 zero. Let's go to 15! floor(15/5) = floor(3) = 3 So, 15! ends in 3 zeros. Let's move on to 100!. floor(100/5) + floor(100/25) = floor(20) + floor(4) = 20 + 4 = 24 If you went to 200, you would have to use the next power of 5, or 5^3 = 125. The reason this works is that a number ends in 0 if it is divisible by 10. Divisible by 10 means divisible by both 5 and 2. But there are lots of numbers divisible by 2 (half of them). So, we concentrate on the number of times a number is divisible by 5. But there are tricky numbers like 25, which are divisible by 5 twice, so we have to take those into account (or floor(n/25)). Then again, there are numbers that are divisible by 5 three times, like 125, so we have to take them into account. Does this help? Please feel free to write back with any questions you may have. - Doctor Roy, The Math Forum http://mathforum.org/dr.math/ Date: 05/01/2003 at 14:14:27 From: Teresa Subject: Large factorial numbers That worked! Thank you. |
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