Answer:
The greatest common factor between the two terms is 2a.
Step-by-step explanation:
In order to find the greatest common factor (GCF) between two numbers, we list the factors of each term and find the largest number and and amount of variables each term shares.
Starting with 48a^(6), its factors are:
a, a, a, a, a, a (six of them because of the exponent), 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Next, 38a with factors:
a, 1, 2, 19, 38
Looking at these lists, the largest number they have in common is 2, and they only share one instance of the variable a.
Therefore, the GCF of 48a^(6) and 38a is 2a.