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}