MATH SOLVE

2 months ago

Q:
# What is the GCF of 112 and 142?

Accepted Solution

A:

Solution: The GCF of 112 and 142 is 2MethodsHow to find the GCF of 112 and 142 using Prime FactorizationOne way to find the GCF of 112 and 142 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 112?What are the Factors of 142?Here is the prime factorization of 112:24×712^4 × 7^124×71And this is the prime factorization of 142:21×7112^1 × 71^121×711When 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 112 and 142 by multiplying all the matching prime factors to get a GCF of 112 and 142 as 4:Thus, the GCF of 112 and 142 is: 4How to Find the GCF of 112 and 142 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 112 and 142 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, 112 and 142:Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112Factors of 142: 1, 2, 71, 142When 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 112 and 142 would be 2.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 107 and 23?What is the GCF of 14 and 110?What is the GCF of 52 and 59?What is the GCF of 96 and 35?What is the GCF of 129 and 47?