Solution: The GCF of 106 and 58 is 2MethodsHow to find the GCF of 106 and 58 using Prime FactorizationOne way to find the GCF of 106 and 58 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 106?What are the Factors of 58?Here is the prime factorization of 106:21×5312^1 × 53^121×531And this is the prime factorization of 58:21×2912^1 × 29^121×291When 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 106 and 58 by multiplying all the matching prime factors to get a GCF of 106 and 58 as 4:Thus, the GCF of 106 and 58 is: 4How to Find the GCF of 106 and 58 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 106 and 58 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, 106 and 58:Factors of 106: 1, 2, 53, 106Factors of 58: 1, 2, 29, 58When 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 106 and 58 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 76 and 88?What is the GCF of 48 and 104?What is the GCF of 102 and 68?What is the GCF of 57 and 47?What is the GCF of 45 and 81?