Q:

What is the GCF of 56 and 142?

Accepted Solution

A:
Solution: The GCF of 56 and 142 is 2 Methods How to find the GCF of 56 and 142 using Prime Factorization One way to find the GCF of 56 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 56? What are the Factors of 142? Here is the prime factorization of 56: 2 3 × 7 1 2^3 × 7^1 2 3 × 7 1 And this is the prime factorization of 142: 2 1 × 7 1 1 2^1 × 71^1 2 1 × 7 1 1 When 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 56 and 142 by multiplying all the matching prime factors to get a GCF of 56 and 142 as 4: Thus, the GCF of 56 and 142 is: 4 How to Find the GCF of 56 and 142 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 56 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, 56 and 142: Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 142: 1, 2, 71, 142 When 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 56 and 142 would be 2. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 31 and 103? What is the GCF of 107 and 14? What is the GCF of 74 and 146? What is the GCF of 25 and 3? What is the GCF of 71 and 97?