When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

To solve this problem, we need to understand the properties of remainders.

Step 1: First, let's look at the first two conditions. When 242 is divided by the divisor, the remainder is 8. This means that the divisor divides evenly into (242 - 8) = 234.

Step 2: Similarly, when 698 is divided by the divisor, the remainder is 9. This means that the divisor divides evenly into (698 - 9) = 689.

Step 3: The divisor must be a factor of both 234 and 689. The greatest common divisor of these two numbers is 1, which means that the divisor could potentially be 1.

Step 4: However, we have a third condition to consider. When the sum of 242 and 698 (which is 940) is divided by the divisor, the remainder is 4. This means that the divisor divides evenly into (940 - 4) = 936.

Step 5: The divisor must also be a factor of 936. The greatest common divisor of 234, 689, and 936 is 17.

Therefore, the value of the divisor is 17.