Q:

What is the GCF of 40 and 118?

Accepted Solution

A:
Solution: The GCF of 40 and 118 is 2MethodsHow to find the GCF of 40 and 118 using Prime FactorizationOne way to find the GCF of 40 and 118 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 40?What are the Factors of 118?Here is the prime factorization of 40:23×512^3 × 5^123×51And this is the prime factorization of 118:21×5912^1 × 59^121×591When 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 40 and 118 by multiplying all the matching prime factors to get a GCF of 40 and 118 as 4:Thus, the GCF of 40 and 118 is: 4How to Find the GCF of 40 and 118 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 40 and 118 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, 40 and 118:Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40Factors of 118: 1, 2, 59, 118When 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 40 and 118 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 50 and 20?What is the GCF of 30 and 120?What is the GCF of 150 and 101?What is the GCF of 46 and 91?What is the GCF of 130 and 122?