It took me a while to figure out the rules. At first I thought you needed to divide two numbers cleanly with no remainder, and remained thoroughly confused until I checked out the tutorial.
Dividing two numbers by their GCF is novel and clever, but is admittedly unintuitive (both the name "Divide and Conquer" and the logo of an 8 being divided by 4 don't suggest what the game is really about).
It's pretty fun once you get into it. I slowly gained a "feel" for which high numbers shared a GCF, which felt good, like my brain was gliding.
My question is, do you want this to be a "speed" game or a "thinky" game? Because the two sides are at odds with each other.
On one hand, matching numbers quickly feels great, but since you can get an unsolvable board state, and you can't tell what match will make the board unsolvable because you're going so fast, it makes getting the fastest time luck-based.
On the other hand, this would be a great zen game if I weren't being timed. Or, maybe a "Zen Mode" could be one of the options, with no time limit and a board that refills automatically when it becomes unsolvable.