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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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Q: What number can you multiply to get 672?
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