INMO 2004 Problem 5

Let $S$ denote the set of all 6-tuples $(a, b, c, d, e, f)$ of positive integers such that $a^{2}+b^{2}+c^{2}+d^{2}+e^{2}=$ $f^{2}$. Consider the set

$$T=\{a b c d e f:(a, b, c, d, e, f) \in S\}$$

Find the greatest common divisor of all the members of $T$.