MATH SOLVE

1 month ago

Q:
# What is the GCF of 78 and 129?

Accepted Solution

A:

Solution: The GCF of 78 and 129 is 3MethodsHow to find the GCF of 78 and 129 using Prime FactorizationOne way to find the GCF of 78 and 129 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 129?Here is the prime factorization of 78:21×31×1312^1 × 3^1 × 13^121×31×131And this is the prime factorization of 129:31×4313^1 × 43^131×431When 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 129 by multiplying all the matching prime factors to get a GCF of 78 and 129 as 9:Thus, the GCF of 78 and 129 is: 9How to Find the GCF of 78 and 129 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 78 and 129 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 129:Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78Factors of 129: 1, 3, 43, 129When 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 78 and 129 would be 3.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 11 and 73?What is the GCF of 142 and 135?What is the GCF of 72 and 104?What is the GCF of 51 and 39?What is the GCF of 59 and 105?