Q:

What is the GCF of 45 and 28?

Accepted Solution

A:
Solution: The GCF of 45 and 28 is 1 Methods How to find the GCF of 45 and 28 using Prime Factorization One way to find the GCF of 45 and 28 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 45? What are the Factors of 28? Here is the prime factorization of 45: 3 2 × 5 1 3^2 × 5^1 3 2 × 5 1 And this is the prime factorization of 28: 2 2 × 7 1 2^2 × 7^1 2 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 45 and 28 is 1. Thus, the GCF of 45 and 28 is: 1 How to Find the GCF of 45 and 28 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 45 and 28 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, 45 and 28: Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 28: 1, 2, 4, 7, 14, 28 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 45 and 28 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 30 and 96? What is the GCF of 67 and 22? What is the GCF of 73 and 79? What is the GCF of 102 and 74? What is the GCF of 130 and 9?