MATH SOLVE

1 month ago

Q:
# What is the GCF of 78 and 134?

Accepted Solution

A:

Solution: The GCF of 78 and 134 is 2MethodsHow to find the GCF of 78 and 134 using Prime FactorizationOne way to find the GCF of 78 and 134 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 78?What are the Factors of 134?Here is the prime factorization of 78:21×31×1312^1 × 3^1 × 13^121×31×131And this is the prime factorization of 134:21×6712^1 × 67^121×671When 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 78 and 134 by multiplying all the matching prime factors to get a GCF of 78 and 134 as 4:Thus, the GCF of 78 and 134 is: 4How to Find the GCF of 78 and 134 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 78 and 134 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, 78 and 134:Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78Factors of 134: 1, 2, 67, 134When 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 78 and 134 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 69 and 114?What is the GCF of 146 and 87?What is the GCF of 117 and 144?What is the GCF of 32 and 95?What is the GCF of 82 and 143?