Solution: The GCF of 65 and 29 is 1MethodsHow to find the GCF of 65 and 29 using Prime FactorizationOne way to find the GCF of 65 and 29 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 65?What are the Factors of 29?Here is the prime factorization of 65:51×1315^1 × 13^151×131And this is the prime factorization of 29:29129^1291When 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 65 and 29 is 1.Thus, the GCF of 65 and 29 is: 1How to Find the GCF of 65 and 29 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 65 and 29 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, 65 and 29:Factors of 65: 1, 5, 13, 65Factors of 29: 1, 29When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 65 and 29 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 6 and 113?What is the GCF of 68 and 60?What is the GCF of 12 and 120?What is the GCF of 61 and 134?What is the GCF of 4 and 89?