the sum of two number is 217 and their HCF is 27 . find the number
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HCF (X, Y) = 27
Thus, we can write, X = 27a & Y = 27b; where a & b are co-prime to each other.
Now, X+Y=216
=>27a+27b=216
=>a+b=8
So, we have two conditions with us now. (a + b) is 8 and a and b are co-prime to each other.
Possible pairs of a & b are: (1,7), (3,5)
Thus possible pairs of the numbers are (27, 189) & (81, 135)
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Answer:
Let the no. be x and y in this case .
HCF (x,y)=27
Thus, we can write, x=27a and y=27b where a and b are co-prime to each other .
Now x+y= 217
=> 27a-27b=217
=> a+b= 8
So we have two conditions with us now. (a+b) is 8 and a and b are co-prime to each other.
-possible pairs of a and b = (1,7), (3,5)
Thus possible pairs of the no. are
(27,189) and (81,135).
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