When it comes to solving for the greatest common factor (GCF) of two numbers, there are a few strategies that can be used. In this case, our goal is to determine the GCF of 24 and 32.

One way to approach this problem is to list out all of the factors of each number and identify the largest factor that they have in common. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 32 are 1, 2, 4, 8, 16, and 32. By comparing these lists, we can see that the largest factor that they have in common is 8. Therefore, the GCF of 24 and 32 is 8.

Another method for finding the GCF involves prime factorization. To use this method, we need to write both numbers as products of their prime factors. The prime factorization of 24 is 2 x 2 x 2 x 3, while the prime factorization of 32 is 2 x 2 x 2 x 2 x 2. We can then identify the common factors and multiply them together to find the GCF. In this case, the common factors are 2 x 2 x 2, which equals 8. Again, we get the same result that the GCF of 24 and 32 is 8.

In conclusion, there are multiple ways to solve for the greatest common factor of two numbers. In this case, using either the factor listing method or the prime factorization method, we determined that the GCF of 24 and 32 is 8. Understanding how to find the GCF can be useful in a variety of mathematical applications and problem-solving situations.