document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394328>Question 394328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am thinking of a three digit number. It is an odd multiple of three,and the product of its digits is 24. Its is larger that 225. What are all the numbers I could be thinking of?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279792 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Since the number is an odd multiple of 3, it must be an odd number.  That is because an odd multiple of 3 cannot have a factor of 2.\r<BR>\n" );
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document.write( "List the possible all single digit factorizations of 24:\r<BR>\n" );
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document.write( "8 X 3 X 1<BR>\n" );
document.write( "6 X 4 X 1<BR>\n" );
document.write( "6 X 2 X 2<BR>\n" );
document.write( "4 X 3 X 2\r<BR>\n" );
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document.write( "We can exclude 6 X 2 X 2 because it does not contain an odd digit hence you cannot form an odd 3 digit number.\r<BR>\n" );
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document.write( "We can exclude 6 X 4 X 1 because 6 + 4 + 1 is not divisible by 3, hence no three digit number formed from those digits will be divisible by 3.\r<BR>\n" );
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document.write( "8, 3, and 1 can be arranged in 6 different orders:\r<BR>\n" );
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document.write( "831, 813, 381, 318, 183, 138.\r<BR>\n" );
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document.write( "Exclude 318 because it is even and exclude 183 and 138 because they are less than 225.\r<BR>\n" );
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document.write( "So, 831, 813, and 381 are all possible.\r<BR>\n" );
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document.write( "4,3, and 2 can be arranged in 6 different ways (finding the ways is left as an exercise for the student.  All of the 6 ways will be larger than 225, but only two of the ways are odd numbers.\r<BR>\n" );
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document.write( "All together you have 5 different possibilities.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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