Solution: The GCF of 106 and 75 is 1MethodsHow to find the GCF of 106 and 75 using Prime FactorizationOne way to find the GCF of 106 and 75 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 75?Here is the prime factorization of 106:21×5312^1 × 53^121×531And this is the prime factorization of 75:31×523^1 × 5^231×52When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 106 and 75 is 1.Thus, the GCF of 106 and 75 is: 1How to Find the GCF of 106 and 75 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 106 and 75 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 75:Factors of 106: 1, 2, 53, 106Factors of 75: 1, 3, 5, 15, 25, 75When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 106 and 75 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 113 and 34?What is the GCF of 47 and 140?What is the GCF of 117 and 121?What is the GCF of 79 and 129?What is the GCF of 3 and 16?