Final answer:
The greatest common factor of 6m and 9m^2 is 3m, which is the largest expression that both terms have in common and can be divided evenly by.
Step-by-step explanation:
To find the greatest common factor (GCF) of 6m and 9m2, we can list the factors of each expression and find the largest factor that they have in common.
- Factors of 6m: 1, 2, 3, 6, m, 2m, 3m, 6m
- Factors of 9m2: 1, 3, 9, m, 3m, 9m, m2, 3m2, 9m2
The common factors of 6m and 9m2 are 1, 3, m, and 3m. The greatest common factor is the largest of these: 3m. This means that 3m is the largest expression that can divide both 6m and 9m2 without leaving a remainder.