document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891345>Question 891345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the following equation, A, B, C, and D are all positive integers such that A has 4 factors, B has 6 factors, and D has 8 factors. What is the smallest possible sum of A, B, C, and D, if (A×B)/C = D ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539677 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rearrange to AB = CD\r<BR>\n" );
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document.write( "Since D has 8 factors, D can equal p^7 or (p^3)(q^1) or pqr where p, q, r are primes.\r<BR>\n" );
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document.write( "Similarly, A is of the form p^3 or pq, and B is of the form p^5 or (p^2)q.\r<BR>\n" );
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document.write( "Greedily let D = (2^3)(3) = 24, A = 2*3 = 6, B = (2^2)(3) = 12, so C = 3. A+B+C+D = 6+12+3+24 = 45. </SPAN>\n" );
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