One way to find the GCF of 78 and 130 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
Here is the prime factorization of 78:
And this is the prime factorization of 130:
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 78 and 130 by multiplying all the matching prime factors to get a GCF of 78 and 130 as 676:
Thus, the GCF of 78 and 130 is: 676