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mn | (2008 x 2009 x 2010)

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April 28, 2009
real analysisfunctionnumber theoryrelatively prime

Problem Statement

For how many ordered pairs of positive integers (m,n) (m,n), m⋅n m \cdot n divides 2008⋅2009⋅2010 2008 \cdot 2009 \cdot 2010 ?
<spanclass=′latex−bold′>(A)</span> 2⋅37⋅5<spanclass=′latex−bold′>(B)</span> 25⋅3⋅5<spanclass=′latex−bold′>(C)</span> 25⋅37⋅5<spanclass=′latex−bold′>(D)</span> 23⋅35⋅52<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 2\cdot3^7\cdot 5 \qquad<span class='latex-bold'>(B)</span>\ 2^5\cdot3\cdot 5 \qquad<span class='latex-bold'>(C)</span>\ 2^5\cdot3^7\cdot 5 \qquad<span class='latex-bold'>(D)</span>\ 2^3\cdot3^5\cdot 5^2 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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