A weird tetrahedron? No?

Geometry Level 3

Let \(V\) be the volume of a tetrahedron bounded by the coordinate planes and the plane \( \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1\) where \(a\),\(b\),\(c\) are positive real numbers.

If \(V\) can be written in the form of
\[ \large \frac{2^{\zeta}a^{\alpha}b^{\beta}c^{\gamma} } {144^{\xi}} \]

where \(\zeta, \alpha, \gamma\) and \(\xi\) are positive integers, what is the value of \( 50\lfloor \zeta + \alpha + \beta + \gamma + \xi \rfloor \)?

Image Credit: Wikimedia Symmetries of the tetrahedron.

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