One way to find the GCF of 105 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 105:
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 105 and 10 by multiplying all the matching prime factors to get a GCF of 105 and 10 as 25:
Thus, the GCF of 105 and 10 is: 25