Q:

What is the GCF of 17 and 45?

Accepted Solution

A:
Solution: The GCF of 17 and 45 is 1 Methods How to find the GCF of 17 and 45 using Prime Factorization One way to find the GCF of 17 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 17? What are the Factors of 45? Here is the prime factorization of 17: 1 7 1 17^1 1 7 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 17 and 45 is 1. Thus, the GCF of 17 and 45 is: 1 How to Find the GCF of 17 and 45 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 17 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, 17 and 45: Factors of 17: 1, 17 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 17 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 8 and 15? What is the GCF of 125 and 26? What is the GCF of 66 and 10? What is the GCF of 96 and 36? What is the GCF of 130 and 75?