document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73701>Question 73701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P denote the product of all the positive primes less than 100. What is the units' digit of P?\r<BR>\n" );
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document.write( "I started writing out the primes from 1 to 99, but it took forever and I missed a lot of them. There must be some way to get this answer WITHOUT doing all that math, right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52895 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You got it ... there's an easy way once you think about it a little.  But before that, there are<BR>\n" );
document.write( "25 prime numbers between 1 and 100.  They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,<BR>\n" );
document.write( "43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.<BR>\n" );
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document.write( "Let's look at the product of just two of these primes.  The product of 2 and 5 is, of course,<BR>\n" );
document.write( "10.  After that, what is the units digit of any other multiplication?  10 * 3 = 30. That times<BR>\n" );
document.write( "7 is 210. Times 11 is 2310.  There we have the product of the first 5 primes. And by now you<BR>\n" );
document.write( "can probably see that any additional multiplications will end in zero in the units position (even if you go to the product of the primes out to a million or beyond).<BR>\n" );
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document.write( "Does this help?  Hope so ...<BR>\n" );
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