Firstly, the Mountain Halls takes up 24 squares, so if it increased production by 24 squares that sounds like it would simply be break-even relative to using the space for more factories, which is fine but hardly fantastic (though the pop does add significantly to its value).
Right, at level 1 it takes up 24 squares, and saves 24 squares.
If you have 4 of each factory it saves you 32, if you have 5 of each, it saves 40. All at level 1 mountain halls.
But secondly, are you factoring in the boost relic bonus?
Yes, since the only scenario I tested was with my level 23 factories, I assumed max boost.
your factories produce 800% of the base value, to which level 1 MH adds 24%, which is ~1/33. Doesn't that mean you'd have to have 33 factories before the MH produces as much as simply building another factory would?
This doesn't factor in support buildings. For example, a level 23 gem factory needs roughly
24 squares
2 road tiles
45 squares of workshops (assuming 150% culture)
53 squares of residences for the gem factory
35 squares of residences for the workshops
41 squares of culture for res/ws/gem (assuming 340 culture per square from pole of donations) to get 150% culture
Once you start to factor everything into what you need to run a Gem factory, it's closer to
200 squares than the 24 that the building itself takes up.
That is what I tried to do for each tier, and then see how the Mountain halls compares to the GA.