document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030289>Question 1030289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My mystery number only has the prime factors of 2,3, and 5. It has 18 factors. What are the possibilities for my mystery number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645224 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mystery number would have the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ep%5B1%5D%2A3%5Ep%5B2%5D%2A5%5Ep%5B3%5D ALIGN=MIDDLE  ALT=\"2%5Ep%5B1%5D%2A3%5Ep%5B2%5D%2A5%5Ep%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The number of factors, or divisors, is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29 ALIGN=MIDDLE  ALT=\"%28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29+=+18 ALIGN=MIDDLE  ALT=\"%28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "But 18 = 2*3*3, hence there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%21%29%2F%281%212%21%29+=+3 ALIGN=MIDDLE  ALT=\"%283%21%29%2F%281%212%21%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > possibilities, namely\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=1 ALIGN=MIDDLE  ALT=\"p%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D=2 ALIGN=MIDDLE  ALT=\"p%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B3%5D=2 ALIGN=MIDDLE  ALT=\"p%5B3%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=2 ALIGN=MIDDLE  ALT=\"p%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D=1 ALIGN=MIDDLE  ALT=\"p%5B2%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B3%5D=2 ALIGN=MIDDLE  ALT=\"p%5B3%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=2 ALIGN=MIDDLE  ALT=\"p%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D=2 ALIGN=MIDDLE  ALT=\"p%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B3%5D=1 ALIGN=MIDDLE  ALT=\"p%5B3%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >;\r<BR>\n" );
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document.write( "==> The possibilities for the mystery number are 450, 300, or 180. </SPAN>\n" );
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