One way to find the GCF of 89 and 34 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 89:
And this is the prime factorization of 34:
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 89 and 34 is 1.
Thus, the GCF of 89 and 34 is: 1