the sum of two numbers is 384.What are the possible number if their is HCF 48?

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violy | High School Teacher | (Level 1) Associate Educator

Posted on

Take note that 384 divided by 48 = 8. 

Hence, if we let one of the numbers as 48, the other number which is 

384 - 48 = 336 will still be divisible by 48. 

Hence, the two numbers are 48 and 336

 

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Let number be x and y ( positive integer).

So by given condition 

`x+y=384`     (i)

since HCF of x and y  is 48

therefore

`x xx y=m(48)^2`     (ii)   m is an integer.

`x={m(48)^2}/y`           (iii)

substitute x from (iii) in (i)

`{m(48)^2}/y+y=384`

`m(48)^2+y^2=384y`     (iv)

let  `y=48l`

`therefore `   (iv) reduces to

`m(48)^2+(48l)^2-384xx48l=0`

`l^2-8l+m=0`         (v)

solving (v) for l and m ,we may get many solutions.

m=16 ,l= 4 then  y=192, x=192

m=15 ,l=3 then  y=144 x=240

m=12 ,l= 2 then  y= 96 ,x= 288

m=7 ,l=1 then    y=48, x=336

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