Solution: The GCF of 105 and 40 is 5MethodsHow to find the GCF of 105 and 40 using Prime FactorizationOne way to find the GCF of 105 and 40 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 40?Here is the prime factorization of 105:31×51×713^1 × 5^1 × 7^131×51×71And this is the prime factorization of 40:23×512^3 × 5^123×51When 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 40 by multiplying all the matching prime factors to get a GCF of 105 and 40 as 25:Thus, the GCF of 105 and 40 is: 25How to Find the GCF of 105 and 40 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 105 and 40 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 40:Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 105 and 40 would be 5.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 74 and 137?What is the GCF of 1 and 39?What is the GCF of 3 and 15?What is the GCF of 33 and 85?What is the GCF of 112 and 9?