Solution: The GCF of 150 and 52 is 2MethodsHow to find the GCF of 150 and 52 using Prime FactorizationOne way to find the GCF of 150 and 52 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 150?What are the Factors of 52?Here is the prime factorization of 150:21×31×522^1 × 3^1 × 5^221×31×52And this is the prime factorization of 52:22×1312^2 × 13^122×131When 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 150 and 52 by multiplying all the matching prime factors to get a GCF of 150 and 52 as 4:Thus, the GCF of 150 and 52 is: 4How to Find the GCF of 150 and 52 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 150 and 52 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, 150 and 52:Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150Factors of 52: 1, 2, 4, 13, 26, 52When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 150 and 52 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 140 and 114?What is the GCF of 27 and 93?What is the GCF of 80 and 62?What is the GCF of 72 and 135?What is the GCF of 89 and 97?