Playing with factorials

Have you ever gone through factorial dependent questions in aptitude? Many problems which deal with factorials seems to be too complex and most of us may skip those questions even before a single try.so how can we stop these problems irritating or confusing us? well a few simple procedures to solve all such problems are given here

Before starting the procedures, let us learn about basics...

Factorial(!): Product of an integer with all the integers below it.

e.g: 4! = 4*3*2*1

• The Highest power of a prime number 'P' (P is prime) in factorial of another number 'N' is

N/P + N /P^2 + N/P^3 + .....

•  The Highest power of a number 'P^a' where P is a prime number in N! is
  [ N/P + N/P^2 + N/P^3 .......]/a

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Problem:
What is the highest power of 5 in 100!
Solution:
 =100/5 + 100/25
 = 20 + 4
 = 24

Problem:
What is the highest power of  30 in 120!
Solution:
Prime Factors of 30: 1,2,3,5
Highest prime factor=5
so P=5
 = 120/5 + 120/25
 =24 + 4
 =28
Problem:
What is the highest power of 9 in 90!
Solution:
3^2=9
so P=3
 = [ 90/3 + 90/9 + 90/27 + 90/72 ] /2
 = [ 30 + 10 + 3 + 1 ] /2
 =44/2
 = 22

Practice Questions:
1) What is the highest power of 24 in 200!
2) What is the highest power of 7 in 50!
3) What is the highest power of 121 in 122!
4) What is the highest power of 6 in 50!

Take your own time but don't forget to solve these!