Solution: The GCF of 105 and 47 is 1MethodsHow to find the GCF of 105 and 47 using Prime FactorizationOne way to find the GCF of 105 and 47 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 105?What are the Factors of 47?Here is the prime factorization of 105:31×51×713^1 × 5^1 × 7^131×51×71And this is the prime factorization of 47:47147^1471When 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 105 and 47 is 1.Thus, the GCF of 105 and 47 is: 1How to Find the GCF of 105 and 47 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 105 and 47 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, 105 and 47:Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105Factors of 47: 1, 47When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 105 and 47 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 148 and 95?What is the GCF of 17 and 74?What is the GCF of 20 and 81?What is the GCF of 82 and 149?What is the GCF of 23 and 115?