Hi Kukrejaria,

Here given P is 30! (30 factorial).

Question is :

If 3^k is factor of 30!, then what is the maximum value of k ?

All we need to do is count the number of 3’s in the 30!.

So,

3 , 6, 9, 12, 15,18, 21, 24,27 and 30.

Above is the list, where we find the 3’s in the 30 factorial.

But in the above list,

9, 18 – counts for two three’s because you have 3^2 in it.

and 27 – counts for three 3’s in it, because 3^3 = 27.

So there are totally,  14 three’s in it.

So the answer is C.

Shortcut to find the same would be,

Find 3’s, 3^2’s and 3^3’s like I have done below,

(30/ 3) + (30/ 3^2) + (30 / 3^3)

= 10 + 3 + 1

= 14.

Hope this helps.

Thank you sir!