document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471736>Question 471736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the number of integers between 1 and 250 that are divisible by2,5,7 is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323516 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll denote {x|n} be the set of integers x <= 250 that divide n.\r<BR>\n" );
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document.write( "By inclusion-exclusion principle, the number of integers is {x|2} + {x|5} + {x|7} - {x|2,5} - {x|2,7} - {x|5,7} + {x|2,5,7} (this is so that we don't overcount or undercount certain numbers like 10 or 140).\r<BR>\n" );
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document.write( "Hence, the number of integers is 125 + 50 + 35 - 25 - 17 - 7 + 3 = 164. </SPAN>\n" );
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