Yeh, got it..thanks again!
*here's the method:
Finding the number of powers of a prime number p, in the n!.
The formula is:
\(\frac{n}{p}+\frac{n}{p^2}+\frac{n}{p^3} ... till p^x\leq{n}\)
What is the power of 2 in 25!?
\(\frac{25}{2}+\frac{25}{4}+\frac{25}{8}+\frac{25}{16}=12+6+3+1=22\)
Finding the power of non-prime in n!:
How many powers of 900 are in 50!
Make the prime factorization of the number: \(900=2^2*3^2*5^2\), then find the powers of these prime numbers in the n!.
Find the power of 2:
\(\frac{50}{2}+\frac{50}{4}+\frac{50}{8}+\frac{50}{16}+\frac{50}{32}=25+12+6+3+1=47\)
= \(2^{47}\)
Find the power of 3:
\(\frac{50}{3}+\frac{50}{9}+\frac{50}{27}=16+5+1=22\)
=\(3^{22}\)
Find the power of 5:
\(\frac{50}{5}+\frac{50}{25}=10+2=12\)
=\(5^{12}\)
We need all the prime {2,3,5} to be represented twice in 900, 5 can provide us with only 6 pairs, thus there is 900 in the power of 6 in 50!.
_________________
Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html