Q:

What is the GCF of 82 and 13?

Accepted Solution

A:
Solution: The GCF of 82 and 13 is 1 Methods How to find the GCF of 82 and 13 using Prime Factorization One way to find the GCF of 82 and 13 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 82? What are the Factors of 13? Here is the prime factorization of 82: 2 1 × 4 1 1 2^1 × 41^1 2 1 × 4 1 1 And this is the prime factorization of 13: 1 3 1 13^1 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 82 and 13 is 1. Thus, the GCF of 82 and 13 is: 1 How to Find the GCF of 82 and 13 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 82 and 13 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, 82 and 13: Factors of 82: 1, 2, 41, 82 Factors of 13: 1, 13 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 82 and 13 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 75 and 19? What is the GCF of 47 and 1? What is the GCF of 70 and 84? What is the GCF of 121 and 131? What is the GCF of 96 and 101?