document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174141>Question 174141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your class has just completed a unit on divisibility rules.  One of the students asks why divisibility by numbers other than 3 and 9 can not be tested by dividing the sum of the digits by the tested number.  How do you respond? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129071 by </B><A HREF=/tutors/aboutme.mpl?userid=rajagopalan><B>rajagopalan(174)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rajagopalan><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=rajagopalan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> why divisibility by numbers other than 3 and 9 can not be tested by dividing the sum of the digits by the tested number. <BR>\n" );
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document.write( "Basis: All multiples of 3 (3, 6, 9, 12, 15, 18..etc) have digits which sum up to 3, 6, 9 only in a cyclic fashion. Hence these two digits are amenable to the law of \"Sum and divide\". <BR>\n" );
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document.write( "Other numbers divsible by digits..2, 4, 5, 7 and 8 sum up to odd numbers also ( eg 12 divisible by 2 and 4 sums to 3 an odd number, 16 divisible by 8 sums to 7 an odd number).<BR>\n" );
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document.write( "Hence the 3,6,9 Rule is not extendable to other digits for divisibility test. </SPAN>\n" );
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