Q:

What is the GCF of 31 and 6?

Accepted Solution

A:
Solution: The GCF of 31 and 6 is 1 Methods How to find the GCF of 31 and 6 using Prime Factorization One way to find the GCF of 31 and 6 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 6? Here is the prime factorization of 31: 3 1 1 31^1 3 1 1 And this is the prime factorization of 6: 2 1 × 3 1 2^1 × 3^1 2 1 × 3 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 6 is 1. Thus, the GCF of 31 and 6 is: 1 How to Find the GCF of 31 and 6 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 31 and 6 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 6: Factors of 31: 1, 31 Factors of 6: 1, 2, 3, 6 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 6 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 125 and 117? What is the GCF of 94 and 23? What is the GCF of 85 and 92? What is the GCF of 109 and 40? What is the GCF of 38 and 11?