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?Options23171311
Question
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?Options23171311
Solution
The problem can be solved by using the properties of remainders.
Step 1: We know that when 242 is divided by the divisor, the remainder is 8. This means that the divisor divides 242 - 8 = 234 exactly.
Step 2: Similarly, when 698 is divided by the divisor, the remainder is 9. This means that the divisor divides 698 - 9 = 689 exactly.
Step 3: The sum of the two numbers 242 and 698 is 940. When this is divided by the divisor, the remainder is 4. This means that the divisor divides 940 - 4 = 936 exactly.
Step 4: Now we need to find a number that divides 234, 689, and 936 exactly. The greatest common divisor (GCD) of these three numbers is the required divisor.
Step 5: The GCD of 234, 689, and 936 is 17. So, the divisor is 17.
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