How Many Pairs of Numbers with a Sum of 588 and HCF of 49? 🎉

Provided data tells us that the sum of the two numbers is 588 and their Highest Common Factor (HCF) is 49. This problem falls under the domain of number theory in mathematics where we deal with properties of integers and their relationships.

When we analyze the given information further, we understand that the two numbers are multiples of their HCF, which is 49 in this case. By dividing the sum, 588, by the HCF, 49, we get 12. The factors pairs of 12 are (1,12), (2,6), and (3,4).

Therefore, we can form three pairs of numbers that satisfy the given conditions of having a sum of 588 and an HCF of 49. These pairs are (49, 539), (98, 490), and (147, 441). Each of these pairs indeed adds up to 588 and shares a Highest Common Factor of 49.

In conclusion, the joyous news is that there are three pairs of numbers that fit the criteria of the sum being 588 and the HCF being 49. Math can indeed be fun when we solve puzzles like these!