Q:

What is the GCF of 76 and 31?

Accepted Solution

A:
Solution: The GCF of 76 and 31 is 1 Methods How to find the GCF of 76 and 31 using Prime Factorization One way to find the GCF of 76 and 31 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 31? 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 31: 3 1 1 31^1 3 1 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 31 is 1. Thus, the GCF of 76 and 31 is: 1 How to Find the GCF of 76 and 31 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 76 and 31 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 31: Factors of 76: 1, 2, 4, 19, 38, 76 Factors of 31: 1, 31 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 31 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 34 and 64? What is the GCF of 134 and 145? What is the GCF of 77 and 147? What is the GCF of 56 and 130? What is the GCF of 13 and 43?