To find the greatest common factor (GCF) of 20a^2 and 12a^4, we need to factor each expression into its prime factors and identify the common factors.
First, let's factor 20a^2. We can start by factoring out the greatest common factor of 20 and a^2, which is 4a^2:
20a^2 = 4a^2 * 5
Next, let's factor 12a^4. We can again start by factoring out the greatest common factor of 12 and a^4, which is 12a^4:
12a^4 = 12a^4 * 1
Now we need to identify the common factors between the two expressions. Both expressions contain a factor of 4, a factor of a^2, and a factor of a^4. Therefore, the greatest common factor of 20a^2 and 12a^4 is:
GCF(20a^2, 12a^4) = 4a^2
Therefore, the greatest common factor of 20a^2 and 12a^4 is 4a^2.