Question 257909
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.<br>
Now let's see what the remainders are when each of these x's are divided into 198:
198/7 = 28 (Reminder 2)
198/14 = 14 (Remainder 2)
198/49 = 4 (Remainder 2)
198/98 = 2 (Remainder 2)<br>
So no matter what x is, the remainder is 2 after you divide it into 198.<br>
Actually we could have figured this out pretty quickly:
{{{198/x = (98+100)/x = 98/x + 100/x}}} 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!.