document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=845376>Question 845376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are several positive integers that leave a remainder of 12 when they are divided into 192. Find the smallest three integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509572 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=509572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose 192 is divided by k. Then we can write <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 192 = kn + 12\">, where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large n \in \mathbb{Z}^{+}\">, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 180 = kn\">. Hence k must be a factor of 180. Furthermore, k must be greater than 12, otherwise the remainder would be less than 12. The three smallest factors of 180 greater than 12 are 15, 18, and 20. </SPAN>\n" );
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