Solution: The GCF of 5 and 138 is 1MethodsHow to find the GCF of 5 and 138 using Prime FactorizationOne way to find the GCF of 5 and 138 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 5?What are the Factors of 138?Here is the prime factorization of 5:515^151And this is the prime factorization of 138:21×31×2312^1 × 3^1 × 23^121×31×231When 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 5 and 138 is 1.Thus, the GCF of 5 and 138 is: 1How to Find the GCF of 5 and 138 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 5 and 138 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, 5 and 138:Factors of 5: 1, 5Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 5 and 138 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 44 and 6?What is the GCF of 64 and 7?What is the GCF of 144 and 65?What is the GCF of 87 and 46?What is the GCF of 79 and 22?