Q:

What is the GCF of 31 and 19?

Accepted Solution

A:
Solution: The GCF of 31 and 19 is 1 Methods How to find the GCF of 31 and 19 using Prime Factorization One way to find the GCF of 31 and 19 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 31? What are the Factors of 19? Here is the prime factorization of 31: 3 1 1 31^1 3 1 1 And this is the prime factorization of 19: 1 9 1 19^1 1 9 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 31 and 19 is 1. Thus, the GCF of 31 and 19 is: 1 How to Find the GCF of 31 and 19 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 31 and 19 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, 31 and 19: Factors of 31: 1, 31 Factors of 19: 1, 19 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 31 and 19 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 91 and 98? What is the GCF of 118 and 18? What is the GCF of 113 and 130? What is the GCF of 146 and 139? What is the GCF of 116 and 19?