Factorisations

Probability Level 4

How many solutions for integers aa and bb are there to

a×b=23×34×55×76×117×138×179, a \times b = 2^{3}\times3^{4}\times5^{5}\times7^{6}\times11^{7}\times13^{8}\times17^{9},

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

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