Question 25
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 $T$.
$$
T=\{a b c d e f:(a, b, c, d, e, f) \in S\}
$$
Find the greatest common divisor of all the members of $T$.