Find the exponent of 12 in 50!

Question
Find the exponent of 12 in 50!

Answer
First let us find the exponent of 2 in 50!
= [50/2] + [50/4] + [50/8] + [50/16] + [50/32]
= 25 + 12 + 6 + 3 + 1
= 47.

Now let us find the exponent of 3 in 50!
= [50/3] + [50/9] + [50/27]
= 16 + 5 + 1
= 22 .

So, for every 3, we can find two 2's (as we have 22 3's and 47>22*2 2's) so that 2*2*3 = 12.

Hence, the highest power of 12 in 50! = 22 (using 22 3's and 22*2 = 44 2's).

Hence, Answer = 22.