Which of the following pairs of numbers has a GCF of 1?

The pair of numbers that has a greatest common factor (GCF) of 1 is indeed 15 and 28. To understand this, we need to analyze the factors of each number in the pair.

The factors of 15 are 1, 3, 5, and 15. The factors of 28 are 1, 2, 4, 7, 14, and 28. The only common factor between these two sets of numbers is 1, which means that they share no other common divisors. Thus, their GCF is 1, indicating that they are coprime, meaning they do not have any prime factors in common.

In contrast, the other pairs of numbers each have a GCF greater than 1. For instance, 8 and 12 share common factors (both are divisible by 4), 20 and 30 share common factors (both are divisible by 10), and 24 and 36 share several common factors (both are divisible by 12). This characterization of numbers emphasizes the unique relationship between 15 and 28, confirming that they are indeed coprime with a GCF of 1.