Q:

What is the GCF of 45 and 37?

Accepted Solution

A:
Solution: The GCF of 45 and 37 is 1 Methods How to find the GCF of 45 and 37 using Prime Factorization One way to find the GCF of 45 and 37 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 37? 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 37: 3 7 1 37^1 3 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 37 is 1. Thus, the GCF of 45 and 37 is: 1 How to Find the GCF of 45 and 37 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 45 and 37 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 37: Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 37: 1, 37 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 37 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 37 and 26? What is the GCF of 16 and 98? What is the GCF of 63 and 141? What is the GCF of 5 and 145? What is the GCF of 33 and 132?