Q:

What is the GCF of 84 and 113?

Accepted Solution

A:
Solution: The GCF of 84 and 113 is 1 Methods How to find the GCF of 84 and 113 using Prime Factorization One way to find the GCF of 84 and 113 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 84? What are the Factors of 113? Here is the prime factorization of 84: 2 2 × 3 1 × 7 1 2^2 × 3^1 × 7^1 2 2 × 3 1 × 7 1 And this is the prime factorization of 113: 11 3 1 113^1 11 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 84 and 113 is 1. Thus, the GCF of 84 and 113 is: 1 How to Find the GCF of 84 and 113 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 84 and 113 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, 84 and 113: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 113: 1, 113 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 84 and 113 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 88 and 10? What is the GCF of 45 and 119? What is the GCF of 14 and 107? What is the GCF of 29 and 116? What is the GCF of 131 and 114?