Product of divisors

\[If\quad the\quad product\quad of\quad all\quad divisors\quad of\quad 240\quad is\quad { 2 }^{ \alpha }{ 3 }^{ \beta }{ 5 }^{ \gamma }\\ then\quad find\quad the\quad value\quad of\quad \frac { \alpha +\beta +\gamma }{ 6 } \]

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