Factorial

Factorial

The factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.

For example 5! = 1*2*3*4*5 = 120

Remember it  0! = 1
                       n! = n*(n-1)!
Basically the question came to competition.
Qus.1..What is the maximum power of 2 in 50!
             Or
   How many 2 in 50!
Solution

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

Since every alternate number is multiple of 2

That is twenty five(25) times of 2

Again in

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

Every multiple of 4 is at least two times 2

That is twelve(12) times of 2

Again in

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

Every multiple of 8 is at least two times 3

That is six(6) times of 2

Again in

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

Every multiple of 16 is at least two times 4

That is three(3) times of 2

Again in

50! = 1*2*3*4*5*6*7*8*9*10……………………………………………….50

Every multiple of 32 is at least two times 5

That is one(1) times of 2

Hence 25+12+6+3+1 = 47

Hence there are 47 time 2 in 50!

Qus.2.What is the maximum power of 5 in 50!
             Or
   How many 5 in 50!
Solution

Qus.1..What is the maximum power of 6 in 50!
             Or
   How many 6 in 50!
Solution        6=2*3
                there are minimum of power 2 and 3

Hence there are 22 time 6 in 50!