Numerical CAT

Let \(\overline{CAT}\) be a three digit number with \(C\) being the hundreds digit, \(A\) being the tens digit and \(T\) being the ones digit.

\(\overline{CAT}=(C+A+T)\times C\times A\times T\).

Given that \(T\) is even, what is the value of \(\overline{CAT}\)?

Image Credit: Wikimedia Cat silhouette
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