\(144 \Rightarrow 2^4 \times 3^2\)
\(196 \Rightarrow 2^2 \times 7^2\)
\(150 \Rightarrow 5^2 \times 2 \times 3\)
144 has \(5 \times 3 = 15\) factors.
196 has \(3 \times 3 = 9\) factors, but we need to subtract 3 (1, 2, and 4)
150 has \(2 \times 2 \times 3 = 12 \) factors, but we need to subtract 2 (1 and 2)
So, there are \(15 + 9 + 12 - 3 - 2 = \color{brown}\boxed{31}\) numbers.