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?

Let the divisor be d. Then: 242 = a×d + 8, so 242 - 8 = 234 = a×d. 698 = b×d + 9, so 698 - 9 = 689 = b×d. Also: 242 + 698 = 940 = c×d + 4, so 940 - 4 = 936 = c×d. The divisor d must divide all three: 234, 689, and 936. GCD of 234 and 936: 234 divides 936 (936/234 = 4), so GCD = 234. Factors of 234: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. Since d > remainders (8, 9), and d divides 689, we test: 689/13 = 53 exactly. So d = 13.