document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=327163>Question 327163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone please help me? <BR>\n" );
document.write( "There is a number that has 2,5, and 8 as divisors. This number has exactly seven additional divisors. What is the number?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for your help:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234410 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=234410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There is more than one answer to this problem.  In fact, there are an infinite number of answers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start with 5 times 8 equals 40.  All of the divisors of 40 are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1, 2, 4, 5, 8, 10, 20, and 40, for a total of 8 divisors.  But the number we seek has exactly 10 total divisors.  Hence you can select any prime number other than 2 and 5 which we will call <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> and multiply this number times 40.  Now we will have a number we can call <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> which has exactly 10 divisors, to wit: 1, 2, 4, 5, 8, 10, 20, 40, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 40p\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For example:  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ 7\">.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 280\">.  The prime factorization of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 280\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^3,\ 5,\ 7\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ 11\">.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 440\">, the prime factorization of which is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^3,\ 5,\ 11\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And so on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );