document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042995>Question 1042995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that, if d is a factor of x,and d is also a factor of y<BR>\n" );
document.write( "where d>=1,x>=1,y>=1 &#8712; Z<BR>\n" );
document.write( "then d^2 is a factor of x multiplied by y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658069 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since d is a factor of x, there exists a positive integer e<BR>\n" );
document.write( "such that x = d*e .<BR>\n" );
document.write( "Since d is a factor of y, there exists a positive integer f<BR>\n" );
document.write( "such that y = d*f .<BR>\n" );
document.write( "So x*y = (d*e)(d*f)<BR>\n" );
document.write( "Since order is not important in multiplication<BR>\n" );
document.write( "x*y = (d*d*e*f) or x*y = d^2*e*f<BR>\n" );
document.write( "and d^2 is a factor of x*y </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );