Q:

What is the GCF of 144 and 119?

Accepted Solution

A:
Solution: The GCF of 144 and 119 is 1 Methods How to find the GCF of 144 and 119 using Prime Factorization One way to find the GCF of 144 and 119 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 144? What are the Factors of 119? Here is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 2 And this is the prime factorization of 119: 7 1 × 1 7 1 7^1 × 17^1 7 1 × 1 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 144 and 119 is 1. Thus, the GCF of 144 and 119 is: 1 How to Find the GCF of 144 and 119 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 144 and 119 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, 144 and 119: Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 119: 1, 7, 17, 119 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 144 and 119 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 26 and 69? What is the GCF of 4 and 116? What is the GCF of 81 and 13? What is the GCF of 84 and 89? What is the GCF of 57 and 37?