Final answer:
The greatest common factor of 7m^4 and 5m^2 is m^2, since m^2 is the highest exponent of m that both terms share.
Step-by-step explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. When variables with exponents are involved, the GCF is the highest exponent both terms share. In this case, we are looking for the GCF of 7m4 and 5m2.
Let's break down both terms:
- 7m4 = 7 × m × m × m × m
- 5m2 = 5 × m × m
The number 7 and 5 have no common factors other than 1, but the m terms do. Both terms have at least an m raised to the power of 2 in common. So, the GCF is m2 (since the lowest exponent of m that is common to both terms is 2).
Therefore, the correct answer is:
C) 5m2