document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612318>Question 612318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the maximum power of 91 for which 3*6*9*12....*228*231 is completely divisible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385700 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=385700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that 91 = 7*13.\r<BR>\n" );
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document.write( "Intuitively there will be fewer multiples of 13 in the set {3,6,...,231}. The multiples of 13 in the set that are less than 231 are 3*13, 6*13, ..., 15*13, five multiples of 13.\r<BR>\n" );
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document.write( "You can find the multiples of 7 but there are definitely more than five of them.\r<BR>\n" );
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document.write( "Therefore the greatest power of 91 that divides 3*6*...*231 is 91^5. </SPAN>\n" );
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