document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047093>Question 1047093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> any number of the form \"abcabc\" must be divisible by which of the following:<BR>\n" );
document.write( "(1)8<BR>\n" );
document.write( "(2)7,13,11<BR>\n" );
document.write( "(3)9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662574 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the answer is selection 2.<BR>\n" );
document.write( "it must be divisible by 7 and 13 and 11.<BR>\n" );
document.write( "i have no idea why.\r<BR>\n" );
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document.write( "it must be means there are no exceptions.\r<BR>\n" );
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document.write( "i took 123123 and divided it by 8 and 9 and did not get integers, so it can't be 8 or 9.\r<BR>\n" );
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document.write( "i took 123123 and divided it by 7 and got an integer.<BR>\n" );
document.write( "i then divided it by 13 and got an integer.<BR>\n" );
document.write( "i then divided it by 11 and got an integer.\r<BR>\n" );
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document.write( "i then took another random number and did the same.\r<BR>\n" );
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document.write( "i took 987987<BR>\n" );
document.write( "same result.<BR>\n" );
document.write( "it was not divisible by 8 or 9.<BR>\n" );
document.write( "it was divisible by 7, 13, and 11.\r<BR>\n" );
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document.write( "i then took 7 * 13 * 11 and got 1001.\r<BR>\n" );
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document.write( "i then divided 123123 by 1001 and got 123\r<BR>\n" );
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document.write( "i then divided 987987 by 1001 and got 987.\r<BR>\n" );
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document.write( "interesting.........\r<BR>\n" );
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document.write( "since 1001 is equal to 1000 + 1, i then looked at:\r<BR>\n" );
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document.write( "123 * 1001 = 123 * (1000 + 1) = 123000 + 123 = 123123.\r<BR>\n" );
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document.write( "i then looked at:\r<BR>\n" );
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document.write( "987 * 1001 = 987 * (1000 + 1) = 987000 + 987 = 987987.\r<BR>\n" );
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document.write( "since abc * 1001 is equal to abc * 1000 + abc * 1 which is equal to abcabc, then:\r<BR>\n" );
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document.write( "abcabc / 1001 is equal to abc.\r<BR>\n" );
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document.write( "since 1001 is equal to (7 * 13 * 11), then:\r<BR>\n" );
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document.write( "abc * 1001 is equal to abc * 7 * 13 * 11 which is then equal to abcabc.\r<BR>\n" );
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document.write( "therefore abcabc / 1001 is equivalent to abcabc / (7 * 13 * 11).\r<BR>\n" );
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document.write( "since it's divisible by 1001, it has to be divisible by the factors of 1001, namely 7, 13, and 11.\r<BR>\n" );
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document.write( "that's what i think is happening.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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