Solution: The GCF of 78 and 120 is 6MethodsHow to find the GCF of 78 and 120 using Prime FactorizationOne way to find the GCF of 78 and 120 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 78?What are the Factors of 120?Here is the prime factorization of 78:21×31×1312^1 × 3^1 × 13^121×31×131And this is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51When 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 78 and 120 by multiplying all the matching prime factors to get a GCF of 78 and 120 as 36:Thus, the GCF of 78 and 120 is: 36How to Find the GCF of 78 and 120 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 78 and 120 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, 78 and 120:Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 78 and 120 would be 6.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 50 and 31?What is the GCF of 97 and 125?What is the GCF of 33 and 26?What is the GCF of 46 and 47?What is the GCF of 129 and 111?