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

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

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 - 8 years, 1 month ago

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

Bhargav Das - 8 years, 1 month ago

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

A Former Brilliant Member - 8 years, 1 month ago

what do you mean?

Aditya Parson - 8 years, 1 month ago

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

A Former Brilliant Member - 8 years, 1 month ago

@A Former Brilliant Member – Oh that, I know how to solve it. I didn't understand your comment, that is it.

Aditya Parson - 8 years, 1 month ago

@Aditya Parson – ok....:)

A Former Brilliant Member - 8 years, 1 month ago

@A Former Brilliant Member – gif and rite and "p and c" are not in my normal vocab, so I didn't get it at first either.

Justin Wong - 8 years, 1 month ago

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

A Former Brilliant Member - 8 years, 1 month ago

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 - 8 years, 1 month 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

Valliappan Ca - 8 years, 1 month ago

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

Tim Ye - 8 years, 1 month 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.

Aditya Parson - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$