Final answer:
The greatest common factor of the expressions 6a^4r^4 and 4a^3 is 2a^3. This is found by taking the GCF of the numeric coefficients (2) and the smallest exponent of 'a' (a^3).
Step-by-step explanation:
The question asks us to find the greatest common factor (GCF) of the expressions 6a4r4 and 4a3. The GCF is the largest expression that divides both terms without leaving a remainder. To find it, we need to compare the coefficients and the powers of the variables one by one.
First, we look at the coefficients: The GCF of 6 and 4 is 2. Next, we compare the powers of 'a'. The term with the smallest exponent of 'a' is a3
Putting it all together, the GCF is 2a3.