System of Equations

Algebra Level 5

If a,b,ca, b, c and dd are 4 positive integers satisfying ab+cd=2371ac+bd=2670ad+bc=2346\begin{aligned} ab+cd & = 2371\\ ac+bd &= 2670 \\ ad+bc &= 2346 \\ \end{aligned}

What is the maximum possible value of a a ?

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