# Comparing fractions: GCD

Number Theory Level 4

$\large \dfrac{\gcd(a+b, b+c, c+a)}{\gcd(a, b, c)}$

Find the sum of all possible values of the fraction above given that $$a,b$$ and $$c$$ are any positive integers.

Clarification: $$\gcd(\cdot)$$ denotes the greatest common divisor function.

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