Solution: The GCF of 33 and 53 is 1MethodsHow to find the GCF of 33 and 53 using Prime FactorizationOne way to find the GCF of 33 and 53 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 33?What are the Factors of 53?Here is the prime factorization of 33:31×1113^1 × 11^131×111And this is the prime factorization of 53:53153^1531When 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 33 and 53 is 1.Thus, the GCF of 33 and 53 is: 1How to Find the GCF of 33 and 53 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 33 and 53 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, 33 and 53:Factors of 33: 1, 3, 11, 33Factors of 53: 1, 53When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 33 and 53 is 1.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 23 and 108?What is the GCF of 59 and 126?What is the GCF of 125 and 37?What is the GCF of 72 and 10?What is the GCF of 138 and 8?