Question

The sum of two numbers is 721 and their H.C.F. is 103. Find the numbers.

Answer 1

Answer:

Let the numbers be X & Y in this case.

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)

Answer 2

Answer:

Let the numbers be X & Y in this case.

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)