Q:

What is the GCF of 115 and 126?

Accepted Solution

A:
Solution: The GCF of 115 and 126 is 1 Methods How to find the GCF of 115 and 126 using Prime Factorization One way to find the GCF of 115 and 126 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 115? What are the Factors of 126? Here is the prime factorization of 115: 5 1 × 2 3 1 5^1 × 23^1 5 1 × 2 3 1 And this is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 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 115 and 126 is 1. Thus, the GCF of 115 and 126 is: 1 How to Find the GCF of 115 and 126 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 115 and 126 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, 115 and 126: Factors of 115: 1, 5, 23, 115 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 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 115 and 126 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 15 and 17? What is the GCF of 98 and 103? What is the GCF of 140 and 50? What is the GCF of 77 and 106? What is the GCF of 89 and 128?