The sum of two numbers is 684 and their HCF is 57. Find all possible pairs of such numbers.

Since, HCF of two numbers = 57
Hence, numbers are multiples of 57
Let, the numbers be 57x and 57y, where x and y are prime to each other.
According to the sum,
57x + 57y = 684
Or, x + y = 12
Hence, required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).
Thus, required pairs of numbers are,
{57 × 1 = 57 and 57 × 11 = 627}

{57 × 5 = 285 and 57 × 7 = 399}