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

We are given that the product of two integers is 289. Hence, let \( x \) and \( y \) be the two integers such that: \[ x \cdot y = 289 \] Since \( 289 = 17^2 \), the possible pairs of factors are: \[ (1, 289), (17, 17) \] Now, compute the sum for each pair:
- For \( (1, 289) \), the sum is \( 1 + 289 = 290 \).
- For \( (17, 17) \), the sum is \( 17 + 17 = 34 \).
Thus, the pair \( (17, 17) \) has the least sum.