One way to find the GCF of 61 and 122 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 61:
And this is the prime factorization of 122:
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 61 and 122 by multiplying all the matching prime factors to get a GCF of 61 and 122 as 3721:
Thus, the GCF of 61 and 122 is: 3721