Q:

What is the GCF of 24 and 142?

Accepted Solution

A:
Solution: The GCF of 24 and 142 is 2MethodsHow to find the GCF of 24 and 142 using Prime FactorizationOne way to find the GCF of 24 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 24?What are the Factors of 142?Here is the prime factorization of 24:23×312^3 × 3^123×31And 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 24 and 142 by multiplying all the matching prime factors to get a GCF of 24 and 142 as 4:Thus, the GCF of 24 and 142 is: 4How to Find the GCF of 24 and 142 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 24 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, 24 and 142:Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Factors 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 24 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 141 and 83?What is the GCF of 39 and 41?What is the GCF of 146 and 80?What is the GCF of 89 and 45?What is the GCF of 118 and 32?