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how to tackle this question?

Expert replies
by magicalhat » Thu Jun 20, 2013 9:35 pm
What is the greatest integer, n, such that 10^n is a factor of 24! ?

I know it requires prime factorization, but I'm stumped after that....
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Source: — Problem Solving |

by srcc25anu » Thu Jun 20, 2013 10:14 pm
First we need to find how many trailing zeroes are in 24!
to find # of trailing zeros = 24 / 5 = 4
so 24! has 4 trailing zeros

4 trailing zeros mean 10^4 therefore n = 4
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by aaggar7 » Fri Jun 21, 2013 1:27 am
Every pair of 5 and 2 will make a 10.

So,we need to calculate the number of 5s and 2s in 24!.
It is better to calculate 5s than 2s because 5s will be less than 2s.

So - 5
10
15
20

Hence n = 4.
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