Which list correctly shows how to find the greatest common factor of three numbers?

To find the greatest common factor (GCF) of three numbers, follow these steps:

1. List the factors: Write out all the factors of each number. Factors of a number are integers that can divide that number without leaving a remainder.

2. Identify common factors: From the lists of factors, identify the common factors—those that appear in each list for all three numbers.

3. Choose the greatest common factor: From the common factors, choose the largest one. This is the greatest common factor.

For example, to find the GCF of 18, 30, and 45, first list the factors of each:

- Factors of 18: 1, 2, 3, 6, 9, 18 - Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 - Factors of 45: 1, 3, 5, 9, 15, 45

Common factors of 18, 30, and 45: 1, 3, 6

The greatest of these is 6, so the GCF of 18, 30, and 45 is 6.

Alternatively, if the numbers are large and listing out factors becomes impractical, you can use the prime factorization method:

1. Find the prime factorization: Break each number down into its prime factors. 2. List the prime factors: Write each number as a product of its prime factors. 3. Identify common prime factors: Look for prime factors that are common to all three numbers. 4. Multiply the common prime factors together: The product of these common prime factors is the GCF.

Let's see this method for the same numbers, 18, 30, and 45:

- Prime factors of 18: 2 × 3 × 3 - Prime factors of 30: 2 × 3 × 5 - Prime factors of 45: 3 × 3 × 5

The only common prime factor to all three numbers is 3, and it appears at least twice in all three numbers. So we take the lowest power of 3 that is common to all, which is 3 × 3 = 9. Note that this is not correct because it doesn't consider the other common factor which is 2, the GCF is actually 2 × 3 = 6.