Finding the number of zero's in 'Factorial of a number'

karthick_prabu

There's a method to find the number of zero's in a 'factorial of a number'.

Formula : round(n/5) + round(n/25) + round(n/125)+.......+round(n/5^n)
Here, round function indicates that only the integer part of (n/5^n) should be taken.

Example1 : Say if you want to find the number of zero's in 5! ??

Usage : In this case n = 5.

-> round(5/5) + round(5/25)+....

->round(1) + round(0)

-> 1 (1 zero in 5!)

Example2 : find the number of zero's in 130! ??

Usage : In this case n = 130.

-> round(130/5) + round(130/25) + round(130/125) ....

->round(36) + round(5) + round(1)

-> 42 (42 zeroes in 130!)

But ma doubt is : can any 1 pls tell me how this formula working ?? put simple : whats the logic of this formula ?

smilingtears

Logic is that you need the combination of 2 and 5 to make a 10..

2*5 = 10..So,if you know how many 5s we have in the required factorial,we can easily find out how many zeroes to expect in that..Number of 2's will be always more than number of fives..so therefore,just knowing how many 5s we have does the job..

waise..isn't this doubt supposed to be on:

http://www.pagalguy.com/forum/quanti...er-system.html (Number System)

karthick_prabu

Ya i completely agree with you that we need to find the number of 5's in the given factorial number.

but, how did the formula --> round(n/5)+round(n/25)+.... arrive?

btwn, thanks for the info smilingtears.

smilingtears · 05:52 AM

Quote:

Originally Posted by karthick_prabu

Ya i completely agree with you that we need to find the number of 5's in the given factorial number.

but, how did the formula --> round(n/5)+round(n/25)+.... arrive?

btwn, thanks for the info smilingtears.

simple chhe..

I'll tell you with an example..

If you want to know how many fives are there in 26!
By convention,you'll go about finding how many fives you have..so you'll divide by 5 n u'll get 5 as the answer..but in reality it has 6 fives.. one from 25 which is equal to 5*5..
Dividing by 5 once will give you the multiples of 5..So,you'll have to divide by 5 again to count for this extra five..

better way to do it is..

find n/5.Now,see if Quotient is greater than 5,if it is..divide it again by 5 n continue till you get a quotient less than 5. It's better than dividing by 25,125(5*5*5) n so on..

Example for 26! as taken above:
no of 5s= 26/5=5(q)+1(r)
discard r=1 n divide 5 by 5 again..you'll get 1..
so answer is 5+1=6

You can use it to find no. of any digit in a factorial
say you want to find number of 2s in 43!

no. of 2s= 43/2=20(q)
since 20> 2 therefore divide again by 2..
so u'll have the series like
20+10+5+2+1
38 twos

karthick_prabu

WOW! amazing explanation.

thanks a lot.

Krack_CAT · 11:18 AM

Quote:

Originally Posted by smilingtears

simple chhe..

I'll tell you with an example..

If you want to know how many fives are there in 26!
By convention,you'll go about finding how many fives you have..so you'll divide by 5 n u'll get 5 as the answer..but in reality it has 6 fives.. one from 25 which is equal to 5*5..
Dividing by 5 once will give you the multiples of 5..So,you'll have to divide by 5 again to count for this extra five..

better way to do it is..

find n/5.Now,see if Quotient is greater than 5,if it is..divide it again by 5 n continue till you get a quotient less than 5. It's better than dividing by 25,125(5*5*5) n so on..

Example for 26! as taken above:
no of 5s= 26/5=5(q)+1(r)
discard r=1 n divide 5 by 5 again..you'll get 1..
so answer is 5+1=6

You can use it to find no. of any digit in a factorial
say you want to find number of 2s in 43!

no. of 2s= 43/2=20(q)
since 20> 2 therefore divide again by 2..
so u'll have the series like
20+10+5+2+1
38 twos

small error on my part..sorry for da useless post

Krack_CAT

Quote:

Originally Posted by karthick_prabu

Example2 : find the number of zero's in 130! ??

Usage : In this case n = 130.

-> round(130/5) + round(130/25) + round(130/125) ....

->round(36) + round(5) + round(1)

-> 42 (42 zeroes in 130!)

small mistake here:
it shd be 26 + 5 + 1
=>32 zeroes in 130!