Solution: The GCF of 59 and 21 is 1MethodsHow to find the GCF of 59 and 21 using Prime FactorizationOne way to find the GCF of 59 and 21 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 59?What are the Factors of 21?Here is the prime factorization of 59:59159^1591And this is the prime factorization of 21:31×713^1 × 7^131×71When 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 59 and 21 is 1.Thus, the GCF of 59 and 21 is: 1How to Find the GCF of 59 and 21 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 59 and 21 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, 59 and 21:Factors of 59: 1, 59Factors of 21: 1, 3, 7, 21When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 59 and 21 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 120 and 26?What is the GCF of 80 and 69?What is the GCF of 5 and 13?What is the GCF of 95 and 149?What is the GCF of 130 and 72?