What are all the factors (all of them!) that determine how much time X number of confirmations of a transaction takes?
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There's an estimated block generation time of 10 minutes, however, due to the randomness of finding the block, there may be an hour gap between blocks followed by 3 within 10 minutes. It's never predictable at a specific given time.
Additionally, miners prefer transactions with fees attached, because the fees are paid back to the miners. This incentive will become more important as the mining reward continues to halve.
There are other factors that do contribute, but the two above are by-far the most influential.