Can two numbers have more than one greatest common factor(GCF)? Why or why not?

No. Greatest means the the largest number.

http://www.mathsisfun.com/greatest-common-factor.html

No, because it’s the greatest common factor

No, two numbers cannot have more than one greatest common factor (GCF). The greatest common factor is defined as the largest positive integer that divides evenly into both numbers. For any given pair of numbers, there is only one largest positive integer that can divide both of them evenly, hence there is only one greatest common factor.

To find the greatest common factor of two numbers, you can follow these steps:

1. List the factors of both numbers: Write down all the positive integers that divide evenly into each number.

For example, if we are finding the GCF of 24 and 36, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

2. Identify the common factors: Look for the positive integers that appear in the factor lists of both numbers.

In our example, the common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12.

3. Determine the greatest common factor: From the list of common factors, identify the largest positive integer.

In our example, the largest common factor of 24 and 36 is 12.

Therefore, the GCF of 24 and 36 is 12. This is the only greatest common factor that these two numbers have.