The highest power of 3 that divides 50! is $3^k$. The value of $k$ is:

Count multiples of each power of 3 up to 50: ⌊50/3⌋ = 16, ⌊50/9⌋ = 5, ⌊50/27⌋ = 1 and ⌊50/81⌋ = 0. Adding them, k = 16 + 5 + 1 = 22. Counting only the multiples of 3 gives the wrong answer 16.