document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118433>Question 118433</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250034/algebrahomeworkh>Pre-Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> write all factors: 165, 129, and 98 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86553 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=86553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to show you how to get started:\r<BR>\n" );
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document.write( "Let's find all the factors of 165:\r<BR>\n" );
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document.write( "First take the square root of 165 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28165%29=12.85 ALIGN=MIDDLE  ALT=\"sqrt%28165%29=12.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now round 12.85 to get 13. This is the number we will stop at.\r<BR>\n" );
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document.write( "So let's ask ourselves...\r<BR>\n" );
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document.write( "Is 1 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F1=165 ALIGN=MIDDLE  ALT=\"165%2F1=165\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in a whole number, this means 1 and 165 are factors of 165.\r<BR>\n" );
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document.write( "Is 2 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F2=82.5 ALIGN=MIDDLE  ALT=\"165%2F2=82.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 2 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 3 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F3=55 ALIGN=MIDDLE  ALT=\"165%2F3=55\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in a whole number, this means 3 and 55 are factors of 165.\r<BR>\n" );
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document.write( "Is 4 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F4=41.25 ALIGN=MIDDLE  ALT=\"165%2F4=41.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 4 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 5 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F5=33 ALIGN=MIDDLE  ALT=\"165%2F5=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in a whole number, this means 5 and 33 are factors of 165.\r<BR>\n" );
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document.write( "Is 6 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F6=27.5 ALIGN=MIDDLE  ALT=\"165%2F6=27.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 6 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 7 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F7=23.5714285714286 ALIGN=MIDDLE  ALT=\"165%2F7=23.5714285714286\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 7 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 8 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F8=20.625 ALIGN=MIDDLE  ALT=\"165%2F8=20.625\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 8 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 9 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F9=18.3333333333333 ALIGN=MIDDLE  ALT=\"165%2F9=18.3333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 9 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 10 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F10=16.5 ALIGN=MIDDLE  ALT=\"165%2F10=16.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 10 is not a factor of 165.\r<BR>\n" );
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document.write( "Is 11 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F11=15 ALIGN=MIDDLE  ALT=\"165%2F11=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in a whole number, this means 11 and 15 are factors of 165.\r<BR>\n" );
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document.write( "Is 12 a factor of 165? Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%2F12=13.75 ALIGN=MIDDLE  ALT=\"165%2F12=13.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <font size=\"4\"><b>not</b></font> result in a whole number, this means 12 is not a factor of 165.\r<BR>\n" );
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document.write( "Remember, stop at 13. Notice how the next factor is 15 and it's already paired with 11 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A11=165 ALIGN=MIDDLE  ALT=\"15%2A11=165\"   DISABLED_style= \"max-width:90%; height:auto;\" >). So this shows that any factor greater than 13 will be paired with it's corresponding factor that is less than 13. This means we only need to test numbers that are less than 13. Essentially this cuts our work in half.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the factors of 165 are\r<BR>\n" );
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document.write( "1, 3, 5, 11, 15, 33, 55, and 165\r<BR>\n" );
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