Solution: The GCF of 120 and 147 is 3MethodsHow to find the GCF of 120 and 147 using Prime FactorizationOne way to find the GCF of 120 and 147 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 120?What are the Factors of 147?Here is the prime factorization of 120:23×31×512^3 × 3^1 × 5^123×31×51And this is the prime factorization of 147:31×723^1 × 7^231×72When 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 120 and 147 by multiplying all the matching prime factors to get a GCF of 120 and 147 as 9:Thus, the GCF of 120 and 147 is: 9How to Find the GCF of 120 and 147 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 120 and 147 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, 120 and 147:Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120Factors of 147: 1, 3, 7, 21, 49, 147When 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 120 and 147 would be 3.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 147 and 29?What is the GCF of 131 and 52?What is the GCF of 129 and 77?What is the GCF of 143 and 135?What is the GCF of 15 and 76?