What's that Number?

Number Theory Level pending

There is a number a b c a b c 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 u + z = 20 , v + y = 20 v + y = 20 , and w + x = 20 w + x = 20 . If a, b, and c are all even digits, and no number in the set ( a , b , c a, b, c ) is repeated, what is the value of a b c a b c abcabc ?

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


The answer is 864864.

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