Thank you for the feedback! That is a good point about the confusing nature of the name and logo; do you think it'd be better if the division sign was removed in the logo (or replaced with something else)?
The main goal is to be as efficient as you can without getting stuck. After playing a few times, the player should slowly be able to develop a strategy and realize which numbers are possible to get "stuck" on (primarily squares of prime numbers like 25, 49, etc...). Another strategy is to quickly identify efficient/optimal reductions such as 92 and 69 --> 4 and 3. This should come more naturally with more practice.
When you say "Zen" mode, are you thinking about something that's different from the current practice mode (non-competitive) or would you just like the timer removed (or an option to hide it) in practice mode so there's less pressure?
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I think a name like "Common Factor" or "GCF" would work well. Maybe for the logo you could show a 21 and a 70, and their GCF 7 between them and slightly under, in a different color. And yeah for the Zen mode, I was thinking of a separate mode with no timer and a board state that resets automatically when unsolvable, kind of like an Endless mode, if that makes sense.