Solution: The GCF of 127 and 101 is 1MethodsHow to find the GCF of 127 and 101 using Prime FactorizationOne way to find the GCF of 127 and 101 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 127?What are the Factors of 101?Here is the prime factorization of 127:1271127^11271And this is the prime factorization of 101:1011101^11011When 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 127 and 101 is 1.Thus, the GCF of 127 and 101 is: 1How to Find the GCF of 127 and 101 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 127 and 101 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, 127 and 101:Factors of 127: 1, 127Factors of 101: 1, 101When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 127 and 101 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 49 and 144?What is the GCF of 124 and 59?What is the GCF of 134 and 150?What is the GCF of 99 and 117?What is the GCF of 123 and 65?