Q:

What is the GCF of 13 and 21?

Accepted Solution

A:
Solution: The GCF of 13 and 21 is 1 Methods How to find the GCF of 13 and 21 using Prime Factorization One way to find the GCF of 13 and 21 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 13? What are the Factors of 21? Here is the prime factorization of 13: 1 3 1 13^1 1 3 1 And this is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 1 × 7 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 13 and 21 is 1. Thus, the GCF of 13 and 21 is: 1 How to Find the GCF of 13 and 21 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 13 and 21 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, 13 and 21: Factors of 13: 1, 13 Factors of 21: 1, 3, 7, 21 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 13 and 21 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 71 and 81? What is the GCF of 92 and 119? What is the GCF of 14 and 116? What is the GCF of 97 and 5? What is the GCF of 15 and 11?