document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983976>Question 983976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i am the number which will make a rectangle 3 times wide, i am the number which has exactly 8 factors, i am the number which has one of my factor as 4, i am the number which is not a multiple of 5 or 7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604770 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"I am the number which will make a rectangle 3 times wide\" may mean that<BR>\n" );
document.write( "if the number is the length of a rectangle,<BR>\n" );
document.write( "it will be twice the whole number measurement of the width of that rectangle.<BR>\n" );
document.write( "In other words, I take that to mean that the number is a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of the mystery number.\r<BR>\n" );
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document.write( "\"I am the number which has one of my factor as 4\" means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=2%5E2 ALIGN=MIDDLE  ALT=\"4=2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of the mystery number.\r<BR>\n" );
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document.write( "\"I am the number which is not a multiple of 5 or 7\" tells us that 5 and 7 are not prime factors of that mystery number, but it is not a particularly useful clue.<BR>\n" );
document.write( "Other prime numbers could be factors, like 11, 13, 17, 19, 23, etc .\r<BR>\n" );
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document.write( "\"I am the number which has exactly 8 factors\" is an important clue.<BR>\n" );
document.write( "A number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=2%5E2 ALIGN=MIDDLE  ALT=\"4=2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > as factors<BR>\n" );
document.write( "has a prime factorization of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=2%5Ea%2A3%5Eb%2A11%5Ec%2A13%5Ed%2A17%5Ee%2A%22...%22 ALIGN=MIDDLE  ALT=\"N=2%5Ea%2A3%5Eb%2A11%5Ec%2A13%5Ed%2A17%5Ee%2A%22...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E=2 ALIGN=MIDDLE  ALT=\"a%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3E=1 ALIGN=MIDDLE  ALT=\"b%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > , with their prime factorizations, range from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=2%5E0%2A3%5E0%2A11%5E0%2A13%5E0%2A17%5E0%2A%22...%22 ALIGN=MIDDLE  ALT=\"1=2%5E0%2A3%5E0%2A11%5E0%2A13%5E0%2A17%5E0%2A%22...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=2%5Ea%2A3%5Eb%2A11%5Ec%2A13%5Ed%2A17%5Ee%2A%22...%22 ALIGN=MIDDLE  ALT=\"N=2%5Ea%2A3%5Eb%2A11%5Ec%2A13%5Ed%2A17%5Ee%2A%22...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "There are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B1%3E=2%2B1=3 ALIGN=MIDDLE  ALT=\"a%2B1%3E=2%2B1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > different possible exponents for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1.=1%2B1=2 ALIGN=MIDDLE  ALT=\"b%2B1.=1%2B1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > different possible exponents for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B1 ALIGN=MIDDLE  ALT=\"c%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > different possible exponents for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2B1 ALIGN=MIDDLE  ALT=\"d%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > different possible exponents for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and so on.<BR>\n" );
document.write( "With all the combined possible choices, we can make<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B1%29%2A%28b%2B1%29%2A%28c%2B1%29%2A%28d%2B1%29%2A%28e%2B1%29%2A%22...%22 ALIGN=MIDDLE  ALT=\"%28a%2B1%29%2A%28b%2B1%29%2A%28c%2B1%29%2A%28d%2B1%29%2A%28e%2B1%29%2A%22...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > has exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=4%2A2 ALIGN=MIDDLE  ALT=\"8=4%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors,<BR>\n" );
document.write( "knowing that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B1%3E=3 ALIGN=MIDDLE  ALT=\"a%2B1%3E=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1%3E=2 ALIGN=MIDDLE  ALT=\"b%2B1%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "it is obvious that it must be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B1=4 ALIGN=MIDDLE  ALT=\"a%2B1=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4-1=3 ALIGN=MIDDLE  ALT=\"a=4-1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B1=2 ALIGN=MIDDLE  ALT=\"b%2B1=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2-1=1 ALIGN=MIDDLE  ALT=\"b=2-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B1=1 ALIGN=MIDDLE  ALT=\"c%2B1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2B1=1 ALIGN=MIDDLE  ALT=\"d%2B1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0 ALIGN=MIDDLE  ALT=\"d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%2B1=1 ALIGN=MIDDLE  ALT=\"e%2B1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=0 ALIGN=MIDDLE  ALT=\"e=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and so on.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=2%5E3%2A3%5E1%2A11%5E0%2A13%5E0%2A17%5E0%2A%22...%22=2%5E3%2A3=8%2A3=highlight%2824%29 ALIGN=MIDDLE  ALT=\"N=2%5E3%2A3%5E1%2A11%5E0%2A13%5E0%2A17%5E0%2A%22...%22=2%5E3%2A3=8%2A3=highlight%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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