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.
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672
There are many possible pair. One such is 1 and 672
It is a composite number.
-628
1234678121416212428324248568496112168224336672