Q:

What is the GCF of 106 and 45?

Accepted Solution

A:
Solution: The GCF of 106 and 45 is 1 Methods How to find the GCF of 106 and 45 using Prime Factorization One way to find the GCF of 106 and 45 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 45? 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 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 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 45 is 1. Thus, the GCF of 106 and 45 is: 1 How to Find the GCF of 106 and 45 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 106 and 45 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 45: Factors of 106: 1, 2, 53, 106 Factors of 45: 1, 3, 5, 9, 15, 45 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 45 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 118 and 99? What is the GCF of 50 and 57? What is the GCF of 146 and 125? What is the GCF of 136 and 52? What is the GCF of 22 and 59?