document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147490>Question 147490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the greatest positive integer n such that 2^n is a factor of 12^10?\r<BR>\n" );
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document.write( "I don't even know where to start!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107868 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=107868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am thinking this:<BR>\n" );
document.write( "We are being asked to find the largest value of n such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E10%2F2%5En ALIGN=MIDDLE  ALT=\"12%5E10%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an integer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E10%2F2%5En ALIGN=MIDDLE  ALT=\"12%5E10%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2A3%29%5E10%2F2%5En ALIGN=MIDDLE  ALT=\"%284%2A3%29%5E10%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%5E10%2A3%5E10%29%2F2%5En ALIGN=MIDDLE  ALT=\"%284%5E10%2A3%5E10%29%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%5E2%29%5E10%2A3%5E10%29%2F2%5En ALIGN=MIDDLE  ALT=\"%28%282%5E2%29%5E10%2A3%5E10%29%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E20%2A3%5E10%29%2F2%5En ALIGN=MIDDLE  ALT=\"%282%5E20%2A3%5E10%29%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2 will never factor into 3, since both are prime. So the largest number for n is the largest one that still results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E20%29%2F2%5En ALIGN=MIDDLE  ALT=\"%282%5E20%29%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > being an integer. What is the smallest number that still is a positive integer? well, that's 1. So what value of n results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E20%29%2F2%5En ALIGN=MIDDLE  ALT=\"%282%5E20%29%2F2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1? n = 20<BR>\n" );
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