Q:

What is the GCF of 49 and 123?

Accepted Solution

A:
Solution: The GCF of 49 and 123 is 1 Methods How to find the GCF of 49 and 123 using Prime Factorization One way to find the GCF of 49 and 123 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 49? What are the Factors of 123? Here is the prime factorization of 49: 7 2 7^2 7 2 And this is the prime factorization of 123: 3 1 × 4 1 1 3^1 × 41^1 3 1 × 4 1 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 49 and 123 is 1. Thus, the GCF of 49 and 123 is: 1 How to Find the GCF of 49 and 123 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 49 and 123 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, 49 and 123: Factors of 49: 1, 7, 49 Factors of 123: 1, 3, 41, 123 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 49 and 123 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 129 and 120? What is the GCF of 97 and 109? What is the GCF of 22 and 102? What is the GCF of 123 and 26? What is the GCF of 23 and 45?