MATH SOLVE

1 month ago

Q:
# What is the GCF of 106 and 72?

Accepted Solution

A:

Solution: The GCF of 106 and 72 is 2MethodsHow to find the GCF of 106 and 72 using Prime FactorizationOne way to find the GCF of 106 and 72 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 106?What are the Factors of 72?Here is the prime factorization of 106:21×5312^1 × 53^121×531And this is the prime factorization of 72:23×322^3 × 3^223×32When 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 106 and 72 by multiplying all the matching prime factors to get a GCF of 106 and 72 as 4:Thus, the GCF of 106 and 72 is: 4How to Find the GCF of 106 and 72 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 106 and 72 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, 106 and 72:Factors of 106: 1, 2, 53, 106Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72When 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 106 and 72 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 4 and 54?What is the GCF of 3 and 89?What is the GCF of 34 and 45?What is the GCF of 142 and 102?What is the GCF of 11 and 125?