document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238461>Question 238461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The total number of prime divisors of the natural number 2002 is:\r<BR>\n" );
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document.write( "(A) 2 (B) 3 (C) 4 (D) 5 (E) None of the above. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175184 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=175184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since 2002 is even it is clearly divisible by 2:<BR>\n" );
document.write( "2002 = 2 * 1001<BR>\n" );
document.write( "Now we look for factors of 1001, if any. Since it is odd, 2 will not divide evenly. And since the digits add up to 2 (1+0+0+1 = 2), it is not divisible by 3. And since 1001 does not end in a 5 or 0, it is not divisible by 5. The next prime is 7. There is no rule for divisibility by 7 so we just have to divide by 7 to see if it works. And it does! Now we have:<BR>\n" );
document.write( "2002 = 2 * 7 * 143<BR>\n" );
document.write( "Now we look for prime factors of 143, if any. 7 does not work on this so we move on to the next prime which is 11. (If there is a rule for divisibility by 11 I am not aware of it.) Dividing 143 by 11 we find that it divides evenly giving us:<BR>\n" );
document.write( "2002 = 2 * 7 * 11 * 13<BR>\n" );
document.write( "The four factors are all prime so your answer is (C). </SPAN>\n" );
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