Solution: The GCF of 27 and 68 is 1MethodsHow to find the GCF of 27 and 68 using Prime FactorizationOne way to find the GCF of 27 and 68 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 27?What are the Factors of 68?Here is the prime factorization of 27:333^333And this is the prime factorization of 68:22×1712^2 × 17^122×171When 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 27 and 68 is 1.Thus, the GCF of 27 and 68 is: 1How to Find the GCF of 27 and 68 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 27 and 68 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, 27 and 68:Factors of 27: 1, 3, 9, 27Factors of 68: 1, 2, 4, 17, 34, 68When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 27 and 68 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 134 and 21?What is the GCF of 13 and 106?What is the GCF of 85 and 149?What is the GCF of 10 and 90?What is the GCF of 12 and 58?