document.write( "Question 752588: when 200 is divided by a positive integer N, the remainder is 5. the number of all possible values of N is:\r
\n" ); document.write( "\n" ); document.write( "A) 2
\n" ); document.write( "B)6
\n" ); document.write( "C)8
\n" ); document.write( "D)13
\n" ); document.write( "E)16\r
\n" ); document.write( "\n" ); document.write( "Thank you very much for looking at this question. I have worked out that N - 40, but I'm not sure how to continue on from there. \n" ); document.write( "
Algebra.Com's Answer #457876 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Suppose we divided N into 200 and got quotient Q and remainder 5,\r\n" );
document.write( "like this:\r\n" );
document.write( "\r\n" );
document.write( "    Q \r\n" );
document.write( "N)200\r\n" );
document.write( "  N·Q\r\n" );
document.write( "    5\r\n" );
document.write( "\r\n" );
document.write( "Then to check that division by multiplying, we'd have\r\n" );
document.write( "200 = N·Q + 5\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "195 = N·Q\r\n" );
document.write( "\r\n" );
document.write( "So we just write down all the possibilities for N and Q,\r\n" );
document.write( "which amounts to writing down all the ways to write 195\r\n" );
document.write( "as a product of two positive integers:\r\n" );
document.write( "\r\n" );
document.write( "195 =   N·Q\r\n" );
document.write( "-------------\r\n" );
document.write( "195 =   1·195\r\n" );
document.write( "195 =   3·65\r\n" );
document.write( "195 =   5·39\r\n" );
document.write( "195 =  13·15\r\n" );
document.write( "195 =  15·13\r\n" );
document.write( "195 =  39·5\r\n" );
document.write( "195 =  65·3\r\n" );
document.write( "195 = 195·1\r\n" );
document.write( "\r\n" );
document.write( "And of course. each of those 8 cases of N gives remainder 5 \r\n" );
document.write( "when we divide 200 by N:\r\n" );
document.write( "\r\n" );
document.write( "   195      65      39      15 \r\n" );
document.write( " 1)200   3)200   5)200  13)200\r\n" );
document.write( "   195     195     195     195\r\n" );
document.write( "     5       5       5       5\r\n" );
document.write( "\r\n" );
document.write( "    13       5       3       1 \r\n" );
document.write( "15)200  39)200  65)200 195)200\r\n" );
document.write( "   195     195     195     195\r\n" );
document.write( "     5       5       5       5\r\n" );
document.write( "\r\n" );
document.write( "Answer:  8\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );