Question

Sum of two number is 36 and their hcf is 4 how many pairs of such numbers are possible

Answer 1

Answer:

8

Step-by-step explanation:

Let, H = HCF

N1 = one number

N2 = another number

x and y = co prime

Hence, N1 = H×x

N2 = H×y

Sum,

N1+N2 = Hx + Hy

= H(x+y)

but, we know, H=4, N1+N2=36

Thus, 36=4(x+y)

x+y=9

So, we have to all possible (x,y) which are co-prime and as well as their sum is 9

(x,y)=(1,8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1)

Therefore we get 8 such possibilities.