View attachment 31035
I would start by rephrasing the problem something like this:
Find the number of ordered pairs (a,b) such that a < b, a and b are relatively prime, and their product is 30!.
I haven't tried solving it yet, but I suspect it will be helpful to find the prime factorization of 30! (or at least to imagine doing so). How might you use that to choose a pair that meets the criteria?
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