Problem solving - 12

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?

A. 10
B. 12
C. 14
D. 16
E. 18

Answer -- C
P = 1*2*3*.....*30
if u factorize P, what is the power of 3 ?
So we have to find out how many 3's are there in he product.
As is known 3,6,9,12,15,18,21,24,27,30 is total count of 10 numbers
but
9 = 3*3 thus 1 extra 3
18 = 3*3*2 thus 1 extra 3
27 = 3*3*3 thus 2 extra 3
Thus in total 10 + 1 + 1 + 2 = 14 3's are there in product.
Hence k is 14.