Q:

What is the GCF of 26 and 97?

Accepted Solution

A:
Solution: The GCF of 26 and 97 is 1 Methods How to find the GCF of 26 and 97 using Prime Factorization One way to find the GCF of 26 and 97 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 26? What are the Factors of 97? Here is the prime factorization of 26: 2 1 × 1 3 1 2^1 × 13^1 2 1 × 1 3 1 And this is the prime factorization of 97: 9 7 1 97^1 9 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 26 and 97 is 1. Thus, the GCF of 26 and 97 is: 1 How to Find the GCF of 26 and 97 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 26 and 97 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, 26 and 97: Factors of 26: 1, 2, 13, 26 Factors of 97: 1, 97 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 26 and 97 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 59 and 104? What is the GCF of 125 and 21? What is the GCF of 113 and 50? What is the GCF of 86 and 38? What is the GCF of 45 and 20?