Q:

What is the GCF of 107 and 26?

Accepted Solution

A:
Solution: The GCF of 107 and 26 is 1 Methods How to find the GCF of 107 and 26 using Prime Factorization One way to find the GCF of 107 and 26 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 107? What are the Factors of 26? Here is the prime factorization of 107: 10 7 1 107^1 10 7 1 And this is the prime factorization of 26: 2 1 × 1 3 1 2^1 × 13^1 2 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 107 and 26 is 1. Thus, the GCF of 107 and 26 is: 1 How to Find the GCF of 107 and 26 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 107 and 26 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, 107 and 26: Factors of 107: 1, 107 Factors of 26: 1, 2, 13, 26 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 107 and 26 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 106? What is the GCF of 110 and 20? What is the GCF of 126 and 145? What is the GCF of 12 and 82? What is the GCF of 42 and 81?