Question
Download Solution PDFThe sum of two numbers is 1224 and their HCF is 68. The number of co-prime pairs satisfying the above condition is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGIVEN:
The sum of two numbers is 1224 and their HCF is 68
CONCEPT USED:
H.C.F = H.C.F of two numbers is the highest possible number that divides both numbers completely
CALCULATION:
Let the two numbers be x and y respectively
It is given that the sum of the two numbers is 1224, therefore
x + y = 1224
Also, 68 is their HCF, thus both numbers must be divisible by 68
So, 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.
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