document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722997>Question 722997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the number that satisfies all three of the following conditions:<BR>\n" );
document.write( "&#61623; it is a composite between 62 and 72;<BR>\n" );
document.write( "&#61623; the sum of the digits is a prime number; and<BR>\n" );
document.write( "&#61623; it has more than four factors. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442980 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=442980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The range of possibilities is very limited.  Some or the possibilities to first consider could be from the set of {62,63,64,65,66,67,68,69,70,71,72}.  It is a COMPOSITE number, so eliminate the primes.   Look in {62,63,64,65,66,68,69,70,72}.  \r<BR>\n" );
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document.write( "Sum of the digits is prime!  This cuts down the possibilities to {65,70}.  6+5=11 prime, and 7+0=7 prime.  \r<BR>\n" );
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document.write( "FOUR FACTORS?  Cannot be 65 because this one only has 5 and 13 as its factors.  The number must be 70 to satisfy all three conditions. 70=7*10 and 70=35*2, but the condition is still not a fit because also 70=14*5.  If you were to rely on a very simple elementary way of thinking, you could choose 65 because in the very elementary sense, the factors of 65 are: 1, 5, 13, and 65.\r<BR>\n" );
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document.write( "ANSWER: Must be 65. </SPAN>\n" );
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