Q:

What is the GCF of 109 and 60?

Accepted Solution

A:
Solution: The GCF of 109 and 60 is 1 Methods How to find the GCF of 109 and 60 using Prime Factorization One way to find the GCF of 109 and 60 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 109? What are the Factors of 60? Here is the prime factorization of 109: 10 9 1 109^1 10 9 1 And this is the prime factorization of 60: 2 2 × 3 1 × 5 1 2^2 × 3^1 × 5^1 2 2 × 3 1 × 5 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 109 and 60 is 1. Thus, the GCF of 109 and 60 is: 1 How to Find the GCF of 109 and 60 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 109 and 60 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, 109 and 60: Factors of 109: 1, 109 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 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 109 and 60 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 34 and 87? What is the GCF of 117 and 43? What is the GCF of 76 and 136? What is the GCF of 20 and 47? What is the GCF of 119 and 49?