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Any of its factors including itself
It is a composite number.
Yes, 672.
There are infinitely many pairs. Pick any non-zero number, X and let Y = 672/X. Then X*Y = X*(672/X) = 672. And, since the choice of X was arbitrary, then there are infinitely many such pairs. There are also infinitely many sets of 3, 4 5, ... numbers which will multiply to 672.
If you are asking for the least common multiple, it is 672