Q:

What is the GCF of 76 and 137?

Accepted Solution

A:
Solution: The GCF of 76 and 137 is 1 Methods How to find the GCF of 76 and 137 using Prime Factorization One way to find the GCF of 76 and 137 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 76? What are the Factors of 137? Here is the prime factorization of 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 1 And this is the prime factorization of 137: 13 7 1 137^1 13 7 1 When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 76 and 137 is 1. Thus, the GCF of 76 and 137 is: 1 How to Find the GCF of 76 and 137 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 76 and 137 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, 76 and 137: Factors of 76: 1, 2, 4, 19, 38, 76 Factors of 137: 1, 137 When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 76 and 137 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 146 and 133? What is the GCF of 121 and 86? What is the GCF of 95 and 43? What is the GCF of 9 and 81? What is the GCF of 59 and 88?