What's that Number?

Number Theory Level pending

There is a number \(abcabc\), which has two sets of three consecutive factors {u, v, w}, and {x, y, z}. Each opposite pair of factors sums to 20, that is, \(u + z = 20\), \(v + y = 20\), and \(w + x = 20\). If a, b, and c are all even digits, and no number in the set (\(a, b, c\)) is repeated, what is the value of \(abcabc\)?

Note: \(abcabc\) represents a six digit number with digits \(a\), \(b\) and \(c\), not \(a \times b \times c \times a\times b \times c\). For consecutive factors, \(u + 1 = v\), \(x + 1 = y\), etc.

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