Question

find the number of zeros in 1148!

Answer 1

10+20+........1140 +one zero from it( 100 + 200 +300......1100)
+ 1000 ( 1zero)

no of terms = 114 + 11 +1

So 126 zeroes

Answer 2

Answer: 229

Step-by-step explanation:

We know that the factorial of n or n! can be represent as :-

$n!=n(n-1)(n-2)(n-3).............3.2.1$

Then, 1148! can be represent as :-

$1148!=1148*1147*1146.............................3*2*1$

Now, the number of tens less than 1148=$114$

[because 1140 is the greatest tens number less than 1148]

Then, the number of zeroes in factorial of any number 'a' is given by :-

$2n+1$, where n is the number of tens less than a.

Therefore, the number of zeroes  in 1148!=$2(114)+1=229$