document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=904939>Question 904939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #548938 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=548938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We consider whole numbers greater than 1 and NOT fractions:<BR>\n" );
document.write( "1) It is a Composite Number when it can be divided evenly<BR>\n" );
document.write( "by numbers other than 1 or itself. <BR>\n" );
document.write( "2) It is a Prime Number when it can't be divided evenly by any number<BR>\n" );
document.write( "(except 1 or itself). <BR>\n" );
document.write( "a) Now we can consider \"The Fundamental Theorem of Arithmetic\", this Theorem states;  \"that every integer greater than 1 either is prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not\"<BR>\n" );
document.write( "Therefore there is only one prime factorization of a composite number.<BR>\n" );
document.write( "You can find the proof on the Internet.<BR>\n" );
document.write( "b) 1 has no prime factors<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );