Find Numbers

@Wulfric (160)
India
January 19, 2007 5:24am CST
Such that their Sum is 216 & HCF is 27.. [Please Also give solution, not only answer]
2 people like this
2 responses
Vijay Ganesh
@vijayganesh (843)
• India
20 Jan 07
According to my calculations, the numbers are 135 and 81. 135 + 81 = 216. As LCM of 135 is 27, 5, 1. LCM of 081 is 27, 3. 1. Hence HCF is 27. Thats it. Is it correct. Thanks.
3 people like this
Wulfric
@Wulfric (160)
• India
20 Jan 07
Good, That's right.. But, there is another possible answer.. Give your method..
2 people like this
Vijay Ganesh
@vijayganesh (843)
• India
27 Jan 07
First, I saw the table of 27. Its Obvious that each number must be a multiple of 27, as 27 is the HCF. Then there comes out only two numbers that is 135 and 81, whose sum is 216 and HCF is 27. This is my method for the solution. Thanks, have a nice day. Bye.
Wulfric
@Wulfric (160)
• India
27 Jan 07
What about 189 & 27.. They also satisfy the condition..!!
1 person likes this
srini_the_creator
@srini_the_creator (196)
• India
26 Jun 07
Let the Numbers be X and Y Since 27 is the H.C.F of those numbers so X = 27*a and Y = 27*b ; Now a and b have no common factors Given Sum of Number is 216 = X + Y = 216 =27*a + 27*b = 216 = a + b = 8 Now possible values of a n b are (1,7) & (3,5) So the possible Numbers are (27,189) & (81,135)