Solution: The GCF of 144 and 74 is 2MethodsHow to find the GCF of 144 and 74 using Prime FactorizationOne way to find the GCF of 144 and 74 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 144?What are the Factors of 74?Here is the prime factorization of 144:24×322^4 × 3^224×32And this is the prime factorization of 74:21×3712^1 × 37^121×371When 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 144 and 74 by multiplying all the matching prime factors to get a GCF of 144 and 74 as 4:Thus, the GCF of 144 and 74 is: 4How to Find the GCF of 144 and 74 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 144 and 74 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, 144 and 74:Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144Factors of 74: 1, 2, 37, 74When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 144 and 74 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 43 and 76?What is the GCF of 123 and 110?What is the GCF of 118 and 86?What is the GCF of 78 and 95?What is the GCF of 92 and 19?