document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210203>Question 1210203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851599 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=851599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to the scratch work that tutor greenestamps has written out.\r<BR>\n" );
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document.write( "Note that he mentioned<BR>\n" );
document.write( "(40+1)(20+1) = 41*21 = 861<BR>\n" );
document.write( "However, it is best to leave it as 41*21<BR>\n" );
document.write( "If you're curious how this formula works, then refer to my response on <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/divisibility/Divisibility_and_Prime_Numbers.faq.question.1207622.html\">this page</a> <BR>\n" );
document.write( "Additionally you can refer to formula (3) of <a  rel=nofollow HREF=\"https://mathworld.wolfram.com/DivisorFunction.html\">this page</a>\r<BR>\n" );
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document.write( "A = number of divisors of 20^20<BR>\n" );
document.write( "B = number of divisors of 20^20 that do not involve 5 (i.e. involve 2's only)<BR>\n" );
document.write( "C = number of divisors of 20^20 that have at least one factor of 5\r<BR>\n" );
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document.write( "A = 41*21<BR>\n" );
document.write( "B = 41\r<BR>\n" );
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document.write( "C = A-B<BR>\n" );
document.write( "C = 41*21 - 41<BR>\n" );
document.write( "C = 41*(21 - 1)<BR>\n" );
document.write( "C = 41*20\r<BR>\n" );
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document.write( "D = probability a divisor of 20^20 has at least one factor of 5<BR>\n" );
document.write( "D = C/A<BR>\n" );
document.write( "D = (41*20)/(41*21)<BR>\n" );
document.write( "D = <font color=red>20/21</font> is the final answer in fraction form.\r<BR>\n" );
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document.write( "20/21 = 0.95238 = 95.238% approximately<BR>\n" );
document.write( "Round this approximate value however needed.<BR>\n" );
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