One way to find the GCF of 2 and 10 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 2:
And this is the prime factorization of 10:
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 2 and 10 by multiplying all the matching prime factors to get a GCF of 2 and 10 as 4:
Thus, the GCF of 2 and 10 is: 4