Solution: The GCF of 32 and 106 is 2MethodsHow to find the GCF of 32 and 106 using Prime FactorizationOne way to find the GCF of 32 and 106 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 32?What are the Factors of 106?Here is the prime factorization of 32:252^525And this is the prime factorization of 106:21×5312^1 × 53^121×531When 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 32 and 106 by multiplying all the matching prime factors to get a GCF of 32 and 106 as 4:Thus, the GCF of 32 and 106 is: 4How to Find the GCF of 32 and 106 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 32 and 106 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, 32 and 106:Factors of 32: 1, 2, 4, 8, 16, 32Factors of 106: 1, 2, 53, 106When 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 32 and 106 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 104 and 94?What is the GCF of 68 and 60?What is the GCF of 85 and 10?What is the GCF of 24 and 55?What is the GCF of 110 and 27?