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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, 8 months ago

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3 votes

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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!.

Stephen New - 4 years, 8 months ago

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24 zeroes as [ 100/5 ] + [ 100/5^2 ] = 24

Bhargav Das - 4 years, 8 months ago

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using...gif....rite...?basic p and c

Riya Gupta - 4 years, 8 months ago

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what do you mean?

Aditya Parson - 4 years, 8 months ago

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@Aditya Parson i simply mean.....GREATEST INTEGER FUNCTION i.e. GIF or step up function...... do i need to xplain the soln...? :)

Riya Gupta - 4 years, 8 months ago

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@Riya Gupta Oh that, I know how to solve it. I didn't understand your comment, that is it.

Aditya Parson - 4 years, 8 months ago

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@Aditya Parson ok....:)

Riya Gupta - 4 years, 8 months ago

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@Riya Gupta gif and rite and "p and c" are not in my normal vocab, so I didn't get it at first either.

Justin Wong - 4 years, 8 months ago

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@Justin Wong its permutations and combinations....:)

Riya Gupta - 4 years, 8 months ago

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Numbers of zeros in factorial is equal to \sum_{i=1}^k \lfloor \frac{n}{5^i} \rfloor where 5^k \leq n

Djordje Marjanovic - 4 years, 8 months ago

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Comment deleted May 09, 2013

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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.

Samuel Queen - 4 years, 8 months ago

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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

Valliappan Ca - 4 years, 8 months ago

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I suggest turning off the "Caps Lock" button. It would make all of us a little happier.

Tim Ye - 4 years, 8 months ago

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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.

Aditya Parson - 4 years, 8 months ago

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