Q:

What is the GCF of 108 and 143?

Accepted Solution

A:
Solution: The GCF of 108 and 143 is 1 Methods How to find the GCF of 108 and 143 using Prime Factorization One way to find the GCF of 108 and 143 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 108? What are the Factors of 143? Here is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 3 3 And this is the prime factorization of 143: 1 1 1 × 1 3 1 11^1 × 13^1 1 1 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 108 and 143 is 1. Thus, the GCF of 108 and 143 is: 1 How to Find the GCF of 108 and 143 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 108 and 143 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, 108 and 143: Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 Factors of 143: 1, 11, 13, 143 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 108 and 143 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 7 and 97? What is the GCF of 140 and 89? What is the GCF of 29 and 113? What is the GCF of 129 and 132? What is the GCF of 35 and 74?