document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130014>Question 130014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi tutors,\r<BR>\n" );
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document.write( "I have a question. May I know how to solve this:\r<BR>\n" );
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document.write( "Find all primes that divide 50!  ?\r<BR>\n" );
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document.write( "If it is 50, I have no problem but 50! is too large.\r<BR>\n" );
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document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94972 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=94972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First expand 50!\r<BR>\n" );
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document.write( "50!=50*49*48*47*46*...*3*2*1\r<BR>\n" );
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document.write( "Notice how 50! is made of the product of the numbers from 1 to 50, including the prime numbers from 1 to 50. So the prime numbers:\r<BR>\n" );
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document.write( "2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,\r<BR>\n" );
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document.write( "are factors of the prime numbers that make up 50! and are factors of the composite numbers that make up 50! (for example 4=2*2, 24=2*2*2*3, and 32=2*2*2*2*2). Remember, any number can be represented as a product of primes.\r<BR>\n" );
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document.write( "So to find the number of primes that divide into 50!, simply count the number of primes from 1 to 50.\r<BR>\n" );
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document.write( "So there are 15 primes that divide into 50!<BR>\n" );
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