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# How to find number of 0's in a factorial?

can anyone tell me how many zero's at the end of 100 factorial and how to calualate it

Note by Sai Venkata Raju Nanduri
4 years, 3 months ago

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We make a 10 by having a 2 and a 5 in the prime factorization. Since we obviously have more 2s than 5s in the prime factorization of 100!, we just need to find to find the number of 5s in the factorization of 100!. Of the first 100 integers 100/5=20 of then contain a 5 and 100/25 contain a second 5. Thus there are a total of 20+4=24 0s at the end of 100!. · 4 years, 3 months ago

24 zeroes as [ 100/5 ] + [ 100/5^2 ] = 24 · 4 years, 3 months ago

using...gif....rite...?basic p and c · 4 years, 3 months ago

what do you mean? · 4 years, 3 months ago

i simply mean.....GREATEST INTEGER FUNCTION i.e. GIF or step up function...... do i need to xplain the soln...? :) · 4 years, 3 months ago

Oh that, I know how to solve it. I didn't understand your comment, that is it. · 4 years, 3 months ago

ok....:) · 4 years, 3 months ago

gif and rite and "p and c" are not in my normal vocab, so I didn't get it at first either. · 4 years, 3 months ago

its permutations and combinations....:) · 4 years, 3 months ago

Numbers of zeros in factorial is equal to \sum_{i=1}^k \lfloor \frac{n}{5^i} \rfloor where 5^k \leq n · 4 years, 3 months ago

Comment deleted May 09, 2013

Yes this is the solution if you mean the number of 0's at the end of N! Observe that 7!=5040 has 2 0's but the method yields 1. · 4 years, 3 months ago

WE HAVE TO FIND THE NUMBER OF 5'S GREATEST INTEGER FUNCTION(100/5) + GREATEST INTEGER FUNCTION(100/5^2 ) SO THER WILL BE 24 ZEROS · 4 years, 3 months ago

I suggest turning off the "Caps Lock" button. It would make all of us a little happier. · 4 years, 3 months ago

He initially typed in "$$29$$ ZEROS",and thought that others were wrong and he was right. So that is why the use of caps. Modified his answer later. · 4 years, 3 months ago