Divide and conquer

Let \(\overline{ABC}\) be a three digit positive integer with \(A>C \ge 0\) and having the property that

\(\overline{ABC} \equiv 0 \mod \overline{CBA}\).

If \(n_1,n_2,\cdots,n_k\) are \(k\) numbers satisfying the above constraints,

Find \(n_1+n_2+\cdots+n_k\)

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