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Algebra Level 5

The function \(f\) defined on the set of ordered pairs of positive integers has the following properties:

(a) For all \(x,\) \(f(x,x) = x.\)

(b) For all \(x\) and \(y,\) \(f(x,y) = f(y,x).\)

(c) For all \(x\) and \(y,\) \((x + y)f(x,y) = yf(x,x+y).\)

Find \(f(52,14).\)

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