document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550228>Question 550228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in how many ways can 100 be written as the sum of two numbers,whose HCF is 1? answer choices 40,20,44,none.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358729 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 50+50=100<BR>\n" );
document.write( "hcf=50<BR>\n" );
document.write( "we know they have to all be odd so 2 cant be a possible factor<BR>\n" );
document.write( "1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99<BR>\n" );
document.write( "below i pointed out the prime numbers <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > 9 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > 15 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" > 21 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > 25 27 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29 ALIGN=MIDDLE  ALT=\"29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31 ALIGN=MIDDLE  ALT=\"31\"   DISABLED_style= \"max-width:90%; height:auto;\" > 33 35 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37 ALIGN=MIDDLE  ALT=\"37\"   DISABLED_style= \"max-width:90%; height:auto;\" > 39 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41 ALIGN=MIDDLE  ALT=\"41\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43 ALIGN=MIDDLE  ALT=\"43\"   DISABLED_style= \"max-width:90%; height:auto;\" > 45 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47 ALIGN=MIDDLE  ALT=\"47\"   DISABLED_style= \"max-width:90%; height:auto;\" > 49 51 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53 ALIGN=MIDDLE  ALT=\"53\"   DISABLED_style= \"max-width:90%; height:auto;\" > 55 57 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=59 ALIGN=MIDDLE  ALT=\"59\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=61 ALIGN=MIDDLE  ALT=\"61\"   DISABLED_style= \"max-width:90%; height:auto;\" > 63 65 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=67 ALIGN=MIDDLE  ALT=\"67\"   DISABLED_style= \"max-width:90%; height:auto;\" > 69 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=71 ALIGN=MIDDLE  ALT=\"71\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73 ALIGN=MIDDLE  ALT=\"73\"   DISABLED_style= \"max-width:90%; height:auto;\" > 75 77 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79 ALIGN=MIDDLE  ALT=\"79\"   DISABLED_style= \"max-width:90%; height:auto;\" > 81 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=83 ALIGN=MIDDLE  ALT=\"83\"   DISABLED_style= \"max-width:90%; height:auto;\" > 85 87 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89 ALIGN=MIDDLE  ALT=\"89\"   DISABLED_style= \"max-width:90%; height:auto;\" > 91 93 95 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=97 ALIGN=MIDDLE  ALT=\"97\"   DISABLED_style= \"max-width:90%; height:auto;\" > 99<BR>\n" );
document.write( "there are 25 odd prime numbers from 1 to 100<BR>\n" );
document.write( "adding the corrisponding numbers to make 100 have proven to have a few duplicates or an HCF higher than 1 as shown below:\r<BR>\n" );
document.write( "\n" );
document.write( "(1) 51+49=100<BR>\n" );
document.write( "hcf=1<BR>\n" );
document.write( "find all the prime numbers from 1 to 100<BR>\n" );
document.write( "(2) 1+99 hcf is 1 <BR>\n" );
document.write( "2 is prime but 2 and 98 have hcf of 2<BR>\n" );
document.write( "(3) 3+97 hcf is 1<BR>\n" );
document.write( " 5+95 hcf is 5<BR>\n" );
document.write( "(5) 7+93 hcf is 1<BR>\n" );
document.write( "(6) 11+89 hcf is 1<BR>\n" );
document.write( "(7) 13+87 hcf is 1<BR>\n" );
document.write( "(8) 17+83 hcf is 1<BR>\n" );
document.write( "(9) 19+81 hcf is 1<BR>\n" );
document.write( "(10) 23+77 hcf is 1<BR>\n" );
document.write( "(11) 29+71 hcf is 1<BR>\n" );
document.write( "(12) 31+69 hcf is 1<BR>\n" );
document.write( "(13) 37+63 hcf is 1<BR>\n" );
document.write( "(14) 41+59 hcf is 1<BR>\n" );
document.write( "(15) 43+57 hcf is 1<BR>\n" );
document.write( "(16) 47+53 hcf is 1<BR>\n" );
document.write( "______________<BR>\n" );
document.write( "53+duplicate <BR>\n" );
document.write( "59+duplicate<BR>\n" );
document.write( "(17) 61+39 hcf is 1<BR>\n" );
document.write( "(18) 67+33 hcf is 1<BR>\n" );
document.write( "71+duplicate<BR>\n" );
document.write( "(19) 73+27 hcf is 1<BR>\n" );
document.write( "(20) 79+21 hcf is 1<BR>\n" );
document.write( "83+duplicate<BR>\n" );
document.write( "97+duplicate<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "i count (20) different ways<BR>\n" );
document.write( "if you were to flip them as in a+b to b+a if that counts as a different way then there are 40 ways\r<BR>\n" );
document.write( "\n" );
document.write( "hmmm just went back over this, accidently counted the 5 thisone i made number 4 so theres only 20 or a possible 40 if numbers were reversed<BR>\n" );
document.write( "(4)9+91=100<BR>\n" );
document.write( "9=1 3 9<BR>\n" );
document.write( "91= 1 7 13<BR>\n" );
document.write( "hcf is 1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );