We can simplify it, $3^{199}-3^{196} = 3^3 \times3^{196} - 3^{196}$
$\qquad = 3^{196} (3^3-1) = 3^{196} (27-1) = 26 \times 3^{196} = {\color{red}{13}} \times 2 \times 3^{196}$
So, the greatest prime factor is $13.$
Correct Answer: A
$\textbf{PS:}$ A prime factor is a natural number, other than 1, whose only factors are 1 and itself.