# Factorisations

How many solutions for integers $$a$$ and $$b$$ are there to

$a \times b = 2^{3}\times3^{4}\times5^{5}\times7^{6}\times11^{7}\times13^{8}\times17^{9},$

where $$\gcd(a,b) = 1$$ and $$a>b>1$$?

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