Question

Amongst all pairs of positive integers with product as 289, find which of the two numbers add up to the least.

Hint:

Quick Tip: When asked to find the pair of integers with the least sum for a given product, look for pairs of factors and compare their sums.

Answer 1

Let \( x \) and \( y \) be two integers whose product is 289, i.e., \( x \cdot y = 289 \). Since \( 289 = 17^2 \), the possible integer factor pairs are \( (1, 289) \) and \( (17, 17) \). The sum for each pair is computed as follows: - For \( (1, 289) \), the sum is \( 1 + 289 = 290 \). - For \( (17, 17) \), the sum is \( 17 + 17 = 34 \). The pair \( (17, 17) \) yields the minimum sum.