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Set a,b,c

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November 21, 2005
countingdistinguishabilitynumber theoryprime numbers

Problem Statement

For how many three-element sets of positive integers {a,b,c}\{a,b,c\} is it true that a×b×c=2310a \times b \times c = 2310?
<spanclass=′latex−bold′>(A)</span> 32<spanclass=′latex−bold′>(B)</span> 36<spanclass=′latex−bold′>(C)</span> 40<spanclass=′latex−bold′>(D)</span> 43<spanclass=′latex−bold′>(E)</span> 45<span class='latex-bold'>(A)</span>\ 32 \qquad <span class='latex-bold'>(B)</span>\ 36 \qquad <span class='latex-bold'>(C)</span>\ 40 \qquad <span class='latex-bold'>(D)</span>\ 43 \qquad <span class='latex-bold'>(E)</span>\ 45
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