The sum of two numbers is 1224 and their HCF is 68. The number of co-prime pairs satisfying the above condition is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 3.
Let the two numbers be x and y respectively
The sum of the two numbers = 1224
⇒ x + y = 1224
Now,
Let x = 68a and y = 68b , (a + b) then
⇒ 68a + 68b = 1224
⇒ 68 (a + b) = 1224
⇒ (a + b) = 18
Therefore, the possible pair of values of x and y which are coprime pairs are (1,17), (5,13), and (7,11)
Thus, the required numbers are (1,17), (5,13), (7,11)
Hence, the number of possible pairs is 3