Q:

What is the GCF of 126 and 61?

Accepted Solution

A:
Solution: The GCF of 126 and 61 is 1 Methods How to find the GCF of 126 and 61 using Prime Factorization One way to find the GCF of 126 and 61 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 126? What are the Factors of 61? Here is the prime factorization of 126: 2 1 × 3 2 × 7 1 2^1 × 3^2 × 7^1 2 1 × 3 2 × 7 1 And this is the prime factorization of 61: 6 1 1 61^1 6 1 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 126 and 61 is 1. Thus, the GCF of 126 and 61 is: 1 How to Find the GCF of 126 and 61 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 126 and 61 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, 126 and 61: Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Factors of 61: 1, 61 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 126 and 61 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 53 and 142? What is the GCF of 37 and 15? What is the GCF of 61 and 147? What is the GCF of 71 and 51? What is the GCF of 140 and 113?