Solution: The GCF of 105 and 42 is 21MethodsHow to find the GCF of 105 and 42 using Prime FactorizationOne way to find the GCF of 105 and 42 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 105?What are the Factors of 42?Here is the prime factorization of 105:31×51×713^1 × 5^1 × 7^131×51×71And this is the prime factorization of 42:21×31×712^1 × 3^1 × 7^121×31×71When 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 105 and 42 by multiplying all the matching prime factors to get a GCF of 105 and 42 as 441:Thus, the GCF of 105 and 42 is: 441How to Find the GCF of 105 and 42 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 105 and 42 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, 105 and 42:Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 7, 21. Since 21 is the largest of these common factors, the GCF of 105 and 42 would be 21.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 38 and 2?What is the GCF of 16 and 130?What is the GCF of 89 and 51?What is the GCF of 83 and 63?What is the GCF of 4 and 50?