Q:

What is the GCF of 31 and 130?

Accepted Solution

A:
Solution: The GCF of 31 and 130 is 1 Methods How to find the GCF of 31 and 130 using Prime Factorization One way to find the GCF of 31 and 130 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 130? Here is the prime factorization of 31: 3 1 1 31^1 3 1 1 And this is the prime factorization of 130: 2 1 × 5 1 × 1 3 1 2^1 × 5^1 × 13^1 2 1 × 5 1 × 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 130 is 1. Thus, the GCF of 31 and 130 is: 1 How to Find the GCF of 31 and 130 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 31 and 130 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 130: Factors of 31: 1, 31 Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130 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 130 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 148 and 79? What is the GCF of 67 and 46? What is the GCF of 139 and 93? What is the GCF of 129 and 73? What is the GCF of 34 and 16?