INFINITE
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Assuming you mean 4 consecutive whole numbers, the answer is number that can be expressed as 4n+10 where n is an integer.
4, if you multiply them.
24 of them.
There are 24 different arrangements of 4 numbers (4 factorial or 4!). If you allow numbers to be repeated then the figure becomes 256 (44)
The limit is infinity if the factors do not have to be whole numbers. If you stipulate that the factors have to be whole numbers, then, yes, for each number, there is a limit to how many factors it has. For example, the number 4 has only 3 whole-number factors: 1, 2, and 4.