Solution: The GCF of 137 and 31 is 1MethodsHow to find the GCF of 137 and 31 using Prime FactorizationOne way to find the GCF of 137 and 31 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 137?What are the Factors of 31?Here is the prime factorization of 137:1371137^11371And this is the prime factorization of 31:31131^1311When 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 137 and 31 is 1.Thus, the GCF of 137 and 31 is: 1How to Find the GCF of 137 and 31 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 137 and 31 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, 137 and 31:Factors of 137: 1, 137Factors of 31: 1, 31When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 137 and 31 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 133 and 50?What is the GCF of 14 and 134?What is the GCF of 75 and 64?What is the GCF of 126 and 86?What is the GCF of 48 and 65?