Solution: The GCF of 71 and 89 is 1MethodsHow to find the GCF of 71 and 89 using Prime FactorizationOne way to find the GCF of 71 and 89 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:What are the Factors of 71?What are the Factors of 89?Here is the prime factorization of 71:71171^1711And this is the prime factorization of 89:89189^1891When 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 71 and 89 is 1.Thus, the GCF of 71 and 89 is: 1How to Find the GCF of 71 and 89 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 71 and 89 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.Let’s take a look at the factors for each of these numbers, 71 and 89:Factors of 71: 1, 71Factors of 89: 1, 89When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 71 and 89 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 85 and 26?What is the GCF of 108 and 50?What is the GCF of 34 and 73?What is the GCF of 56 and 147?What is the GCF of 113 and 138?