Solution: The GCF of 63 and 138 is 3MethodsHow to find the GCF of 63 and 138 using Prime FactorizationOne way to find the GCF of 63 and 138 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 63?What are the Factors of 138?Here is the prime factorization of 63:32×713^2 × 7^132×71And this is the prime factorization of 138:21×31×2312^1 × 3^1 × 23^121×31×231When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 63 and 138 by multiplying all the matching prime factors to get a GCF of 63 and 138 as 9:Thus, the GCF of 63 and 138 is: 9How to Find the GCF of 63 and 138 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 63 and 138 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, 63 and 138:Factors of 63: 1, 3, 7, 9, 21, 63Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 63 and 138 would be 3.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 92 and 28?What is the GCF of 34 and 129?What is the GCF of 136 and 93?What is the GCF of 60 and 6?What is the GCF of 137 and 13?