Q:

What is the GCF of 106 and 129?

Accepted Solution

A:
Solution: The GCF of 106 and 129 is 1 Methods How to find the GCF of 106 and 129 using Prime Factorization One way to find the GCF of 106 and 129 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 106? What are the Factors of 129? Here is the prime factorization of 106: 2 1 × 5 3 1 2^1 × 53^1 2 1 × 5 3 1 And this is the prime factorization of 129: 3 1 × 4 3 1 3^1 × 43^1 3 1 × 4 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 106 and 129 is 1. Thus, the GCF of 106 and 129 is: 1 How to Find the GCF of 106 and 129 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 106 and 129 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, 106 and 129: Factors of 106: 1, 2, 53, 106 Factors of 129: 1, 3, 43, 129 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 106 and 129 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 127 and 31? What is the GCF of 97 and 131? What is the GCF of 43 and 122? What is the GCF of 2 and 101? What is the GCF of 86 and 76?