Q:

What is the GCF of 105 and 122?

Accepted Solution

A:
Solution: The GCF of 105 and 122 is 1 Methods How to find the GCF of 105 and 122 using Prime Factorization One way to find the GCF of 105 and 122 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 105? What are the Factors of 122? Here is the prime factorization of 105: 3 1 × 5 1 × 7 1 3^1 × 5^1 × 7^1 3 1 × 5 1 × 7 1 And this is the prime factorization of 122: 2 1 × 6 1 1 2^1 × 61^1 2 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 105 and 122 is 1. Thus, the GCF of 105 and 122 is: 1 How to Find the GCF of 105 and 122 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 105 and 122 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, 105 and 122: Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 Factors of 122: 1, 2, 61, 122 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 105 and 122 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 131 and 10? What is the GCF of 125 and 127? What is the GCF of 45 and 76? What is the GCF of 100 and 103? What is the GCF of 57 and 101?