document.write( "Question 770086: if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the remainder is 2. what is the value of N? \n" ); document.write( "
Algebra.Com's Answer #469305 by ramkikk66(644)\"\" \"About 
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document.write( "if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the remainder is 2. what is the value of N?\r\n" );
document.write( "Ans:\r\n" );
document.write( "N divided by 7 gives remainder 4. So N can be written as 7*m + 4 for some integer m.\r\n" );
document.write( "N divided by 8 gives remainder 2. So N can be written as 8*n + 2 for some integer n.\r\n" );
document.write( "Equating the 2 expressions for N\r\n" );
document.write( "7*m + 4 = 8*n + 2\r\n" );
document.write( "7*m + 2 = 8*n\r\n" );
document.write( "Need to find which integer values of m and n satisfy the above equation. Since it\r\n" );
document.write( "is only 1 equation with 2 unknown variables m and n, we can do it only by trial\r\n" );
document.write( "and error. Try different values for m (1,2,3..) and see if we get an integer \r\n" );
document.write( "value for n.\r\n" );
document.write( "We see that one possible solution is m = 2, n = 2\r\n" );
document.write( "7*2 + 2 = 8*2\r\n" );
document.write( "So the number N is 7*m + 4 = 18.\r\n" );
document.write( "Check: 18 div by 7 gives remainder 4, 18 div by 8 gives remainder 2 :)\r\n" );
document.write( "There are other solutions too - e.g. 74 also gives 4 as remainder when divided\r\n" );
document.write( "by 7 and a remainder of 2 when divided by 8. But 18 is the smallest such number.\r\n" );
document.write( ":)\r\n" );
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