The function \(f\), defined on the set of ordered pairs of positive integers, satisfies the following properties: $$ \begin{eqnarray*}f(x,x) &=& x,\\ f(x,y) &=& f(y,x),\quad\text{and}\\ (x+y) f(x,y) &=& yf(x,x+y).\end{eqnarray*} $$ Calculate \(f(14,52)\).

(第六届AIME1988 第8题)