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Counting Ordered Pairs

Source: 2012 AMC10B Problem #10

February 23, 2012
AMC

Problem Statement

How many ordered pairs of positive integers (M,N)(M,N) staisfy the equation M6=6N\frac{M}{6}=\frac{6}{N}?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 7\qquad<span class='latex-bold'>(C)</span>\ 8\qquad<span class='latex-bold'>(D)</span>\ 9\qquad<span class='latex-bold'>(E)</span>\ 10
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