[rmgk]

The 2-adic valuation is about how often 2 is a prime factor of a number.

For just 52 for example 2 is a prime factor twice, because (52/2)/2 = 13, which is no longer divisible by 2.

Or in other words 52! / (2^49) is an integer, but 52! / (2^50) is not, thus 49 is the correct answer.