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  • Number of zeros in (50)! equals Option: 1 10 Option: 2 11 <div

Number of zeros in (50)! equals 

Option: 1

10 


Option: 2

11 


Option: 3

12 


Option: 4

13 


Answers (1)

best_answer

Exponent of Prime P in n!

Where [x] stands for greatest integer value of x\epsilon R.

If m is the index of highest power of a prime p that divides n! then 

m=\left[\frac{n}{p} \right ]+\left[\frac{n}{p^{2}} \right ]+\left[\frac{n}{p^{3}} \right ]+.............

 

Now,

Zero is generated at the end of a number if it has a factor of 10,

And 10 is formed by multiplication of 2 and 5 . 

So powers of 2 and 5 will decide the number of zeros at the end

Exponent of 2 = \left [ \frac{50}{2} \right ]+ \left [ \frac{50 }{2^2} \right ]+ \left [ \frac{50 }{2^3} \right ]+ \left [ \frac{50 }{2^4} \right ]+ \left [ \frac{50 }{2^5} \right ] ...= 47

Exponent of 5 = \left [ \frac{50}{5} \right ]+ \left [ \frac{50 }{5^2} \right ]... = 12

thus, number of zeros should be 12

Posted by

Ritika Jonwal

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