document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550112>Question 550112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The natural number n is the smallest number satisfying the following properties: when divided by 3 remainder is 1,when divided by 4 remainder is 2,when divided by 5 remainder is 3,when divided by 6 remainder is 4,what is the remainder in case of division by 7? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358462 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=358462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remainders for different numbers divided by different numbers run in patterns.  Start with 3.\r<BR>\n" );
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document.write( "4/3 = 1 R 1, 5/3= 1 R2, 6/3 = 2, 7/3=2R1, 8/3 = 2R2.  Starting from 4 every 3rd number has a remainder of 1 when divided by 3:  4, 7, 10, 13....<P><BR>\n" );
document.write( "Find the pattern of remainders when dividing those by 4.<P><BR>\n" );
document.write( "4/4 = R0, 7/4 = 1R3, 10/4=R2, 13/4=R1, 16/4=R0...22/4=R2...every 12 in the 3's remainder 1 series will have a remainder of 2 when divided by 4.  So that's 10,22,34,46,58...<P><BR>\n" );
document.write( "Find the pattern of remainders when dividing those by 5.<P><BR>\n" );
document.write( "10/5=R0, 22/5=R2, 34/5=R4, 46/5=R1, 58/5=R3, 70/5=R0, 82/5=R2, 94/5=R4, 106/5=R1, 118/5=R3...every 60 in the 4's series will have remainder 3 when divided by 5.  So that's 58, 118, 178, 238, 298...<P><BR>\n" );
document.write( "Find the pattern of remainders when dividing those by 6.<P><BR>\n" );
document.write( "58/6=9R4.  That's the smallest number that has remainder 1 when divided by 3, remainder 2 when divided by 4, R3 when divided by 5, and R4 when divided by 6.<P><BR>\n" );
document.write( "58/7=9 R 2<BR>\n" );
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