One way to find the GCF of 75 and 123 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 75:
And this is the prime factorization of 123:
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 75 and 123 by multiplying all the matching prime factors to get a GCF of 75 and 123 as 9:
Thus, the GCF of 75 and 123 is: 9