Let \( f \) and \( g \) be functions satisfying \( f(x + y) = f(x) f(y),\; f(1) = 7 \) and \( g(x + y) = g(xy),\; g(1) = 1 \), for all \( x, y \in \mathbb{N} \). If \( \sum\limits_{x=1}^{n} \left( \frac{f(x)}{g(x)} \right) = 19607 \), then \( n \) is equal to:
