Q:

What is the GCF of 31 and 132?

Accepted Solution

A:
Solution: The GCF of 31 and 132 is 1 Methods How to find the GCF of 31 and 132 using Prime Factorization One way to find the GCF of 31 and 132 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 132? Here is the prime factorization of 31: 3 1 1 31^1 3 1 1 And this is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 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 31 and 132 is 1. Thus, the GCF of 31 and 132 is: 1 How to Find the GCF of 31 and 132 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 31 and 132 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 132: Factors of 31: 1, 31 Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 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 132 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 32 and 33? What is the GCF of 47 and 35? What is the GCF of 129 and 141? What is the GCF of 46 and 85? What is the GCF of 49 and 57?