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Lucy Yeats
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Homework Statement
N is divisible by 4. N! has exactly 50 zeros. Find N.
Homework Equations
In case anyone younger doesn't know, Y!=Yx(Y-1)x(Y-2)x(Y-3)x...x3x2x1
The Attempt at a Solution
No idea.
Lucy Yeats said:Homework Statement
N is divisible by 4. N! has exactly 50 zeros. Find N.
Homework Equations
In case anyone younger doesn't know, Y!=Yx(Y-1)x(Y-2)x(Y-3)x...x3x2x1
The Attempt at a Solution
No idea.
Lucy Yeats said:Homework Statement
N is divisible by 4. N! has exactly 50 zeros. Find N.
uart said:Lucy, is that 50 trailing zeros or 50 zeros in total?
It's pretty easy to work out how many trailing zeros there are in a factorial without actually calculating the full thing, but I don't know how to find the total number of zero digits any other way.
uart said:Lucy, is that 50 trailing zeros or 50 zeros in total?
It's pretty easy to work out how many trailing zeros there are in a factorial without actually calculating the full thing, but I don't know how to find the total number of zero digits any other way.
berkeman said:Interesting point! From my Excel spreadsheet, that does give two different answers...
Lucy Yeats said:Both.
The teacher said work out n for 50 trailing zeros (which I'm okay with), and n for total zeroes as an 'extension'.
berkeman said:Actually, maybe I'm doing something wrong. I misread the question, and thought it said that N! had to be divisible by 4. Duh, 4 is part of the factorial, so all N! is divisible by 4 for N>=4.
The problem asks for N divisible by 4. And my Excel answer for 50 trailing zeros is not divisible by 4. Hmm. Neither is my Excel answer for 50 zeros total.
berkeman said:Yes, I think Excel is doing okay. I went up through about 54!, and it seems to be calculating things okay. Guess I may go back and do a couple sanity checks, though.
The "Solve N Factorial Puzzle with 50 Zeros" is a mathematical puzzle that involves finding the value of N, where N! (N factorial) has 50 trailing zeros.
This puzzle can be solved by using the concept of prime factorization and the properties of factorial numbers. Essentially, you need to find the prime factors of N and determine how many times each prime factor appears in N!.
The number of trailing zeros in N! is directly related to the number of times 10 can divide into N!. Since 10 is a product of 2 and 5, we need to focus on finding the number of 2s and 5s in the prime factorization of N. This allows us to determine the value of N.
Yes, this puzzle can be solved for any number of zeros. However, the higher the number of zeros, the more difficult the puzzle becomes. For example, finding N for N! with 100 zeros is much more challenging than finding N for N! with 50 zeros.
The "Solve N Factorial Puzzle with 50 Zeros" is a fun and challenging mathematical problem that helps exercise the brain and improve problem-solving skills. Additionally, it showcases the beauty and complexity of mathematics.