2019 AIME II Problem 3

Past Contests AIME 2019 AIME II
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1

Find the number of 7-tuples of positive integers (a, b, c, d, e, f, g) that satisfy the following systems of equations:

\begin{aligned} a b c & =70 \\ c d e & =71 \\ e f g & =72 \end{aligned}