Solution: The GCF of 112 and 120 is 8MethodsHow to find the GCF of 112 and 120 using Prime FactorizationOne way to find the GCF of 112 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 112?What are the Factors of 120?Here is the prime factorization of 112:24×712^4 × 7^124×71And 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 112 and 120 by multiplying all the matching prime factors to get a GCF of 112 and 120 as 4:Thus, the GCF of 112 and 120 is: 4How to Find the GCF of 112 and 120 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 112 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, 112 and 120:Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112Factors 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, 4, 8. Since 8 is the largest of these common factors, the GCF of 112 and 120 would be 8.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 69 and 58?What is the GCF of 133 and 127?What is the GCF of 143 and 41?What is the GCF of 40 and 100?What is the GCF of 129 and 141?