Solution: The GCF of 120 and 110 is 10MethodsHow to find the GCF of 120 and 110 using Prime FactorizationOne way to find the GCF of 120 and 110 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 120?What are the Factors of 110?Here is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51And this is the prime factorization of 110:21×51×1112^1 × 5^1 × 11^121×51×111When 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 120 and 110 by multiplying all the matching prime factors to get a GCF of 120 and 110 as 100:Thus, the GCF of 120 and 110 is: 100How to Find the GCF of 120 and 110 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 120 and 110 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, 120 and 110:Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 5, 10. Since 10 is the largest of these common factors, the GCF of 120 and 110 would be 10.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 125 and 29?What is the GCF of 135 and 30?What is the GCF of 133 and 131?What is the GCF of 65 and 10?What is the GCF of 74 and 91?