PS

IMO C

I'll give you two ways to solve this problem pick whichever you are comfortable with:

1. Write down all the factors of 3 from 1-30
3,6,9,12,15,18,21,24,27,30

Now count how many 3 go into each of the numbers and add them up

1+1+2+1+1+2+1+1+3+1 = 14

2. To find the max power of a prime p present in any factorial f simply find

f/p + f/(p^2) + ..+ f/(p^n)
where p^n < f

So in this case we need to find the value of 30/3+30/(3)^2+30/(3)^3
(we stop at 3^3 since 3^4 > 30)

10+3+1 = 14 approx

yes 14

10 multiples of 3
3 multiple of 9
1 multiple of 27