the sum of two numbers is 384.What are the possible number if their is HCF 48?
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.
Let number be x and y ( positive integer).
So by given condition
since HCF of x and y is 48
`x xx y=m(48)^2` (ii) m is an integer.
substitute x from (iii) in (i)
`therefore ` (iv) reduces to
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