document.write( "Question 257909: If 100 is divided by the positive integer x, the remainder is 2. What is the remainder when 198 is divided by x? \n" ); document.write( "

Algebra.Com's Answer #189934 by jsmallt9(3758) $\"\"$ $\"About$

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If the remainder is 2 when 100 is divided by x then x must divide evenly into 98. The prime factorization of 98 is 2*7*7. X could be any combination of these factors except 2. (X cannot be two or it would divide evenly into 100.) X could be 7, 2*7, 7*7 or 2*7*7.

\n" ); document.write( "Now let's see what the remainders are when each of these x's are divided into 198:
\n" ); document.write( "198/7 = 28 (Reminder 2)
\n" ); document.write( "198/14 = 14 (Remainder 2)
\n" ); document.write( "198/49 = 4 (Remainder 2)
\n" ); document.write( "198/98 = 2 (Remainder 2)

\n" ); document.write( "So no matter what x is, the remainder is 2 after you divide it into 198.

\n" ); document.write( "Actually we could have figured this out pretty quickly:
\n" ); document.write( " $\"198%2Fx+=+%2898%2B100%29%2Fx+=+98%2Fx+%2B+100%2Fx\"$ Since x divides evenly into 98, 98/x is a whole number. That leaves 100/x which, we already knew, has a remainder of 2!. \n" ); document.write( "

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