Hi,
Number of 0s will depend upon number of 5s..
1) number of 5s= \(\frac{1142}{5}+\frac{348}{5}+\frac{17}{5}\)=228+69+3=300..
2) number of 25s=\(\frac{1142}{25}+\frac{348}{25}+\frac{17}{25}\)=45+13=58..
3) number of 125s=\(\frac{1142}{125}+\frac{348}{125}+\frac{17}{125}\)=9+2=11..
4) number of 625s=\(\frac{1142}{625}+\frac{348}{625}+\frac{17}{625}\)=1..

Total number of 5s= 300+58+11+1=370

Ans 370..

It seems you have not put the choices in order and that is why 370 is in D choice and not B..
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I've updated the correct OA. Thanks for pointing out.

Cheers.
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Hi sawata4s,
To find the number of zero’s in a factorial, we get to understand, “how we get tens (zero’s) in a factorial?”
We get 10 when we have a minimum of one “2” and one “5”,
10 = 2 * 5
2’s and 5’s in a combination will give us the number of 10’s,
For every “2” in a factorial we may not have a “5”, but for every “5” in a factorial we will have “2”,
So we can just find the number of five’s to evaluate the number of zero’s
There are multiple ways to do that,
you can see the below image for solving it,
So the answer is B.
Hope this helps

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