Solution: The GCF of 86 and 126 is 2MethodsHow to find the GCF of 86 and 126 using Prime FactorizationOne way to find the GCF of 86 and 126 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 86?What are the Factors of 126?Here is the prime factorization of 86:21×4312^1 × 43^121×431And this is the prime factorization of 126:21×32×712^1 × 3^2 × 7^121×32×71When 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 86 and 126 by multiplying all the matching prime factors to get a GCF of 86 and 126 as 4:Thus, the GCF of 86 and 126 is: 4How to Find the GCF of 86 and 126 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 86 and 126 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, 86 and 126:Factors of 86: 1, 2, 43, 86Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 86 and 126 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 45 and 39?What is the GCF of 48 and 51?What is the GCF of 12 and 85?What is the GCF of 133 and 82?What is the GCF of 102 and 100?