Solution: The GCF of 4 and 77 is 1MethodsHow to find the GCF of 4 and 77 using Prime FactorizationOne way to find the GCF of 4 and 77 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 4?What are the Factors of 77?Here is the prime factorization of 4:222^222And this is the prime factorization of 77:71×1117^1 × 11^171×111When 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 4 and 77 is 1.Thus, the GCF of 4 and 77 is: 1How to Find the GCF of 4 and 77 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 4 and 77 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, 4 and 77:Factors of 4: 1, 2, 4Factors of 77: 1, 7, 11, 77When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 4 and 77 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 53 and 89?What is the GCF of 121 and 101?What is the GCF of 16 and 54?What is the GCF of 23 and 85?What is the GCF of 86 and 42?