Q:

What is the GCF of 37 and 72?

Accepted Solution

A:
Solution: The GCF of 37 and 72 is 1 Methods How to find the GCF of 37 and 72 using Prime Factorization One way to find the GCF of 37 and 72 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 37? What are the Factors of 72? Here is the prime factorization of 37: 3 7 1 37^1 3 7 1 And this is the prime factorization of 72: 2 3 × 3 2 2^3 × 3^2 2 3 × 3 2 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 37 and 72 is 1. Thus, the GCF of 37 and 72 is: 1 How to Find the GCF of 37 and 72 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 37 and 72 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, 37 and 72: Factors of 37: 1, 37 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 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 37 and 72 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 133 and 80? What is the GCF of 134 and 44? What is the GCF of 6 and 138? What is the GCF of 102 and 57? What is the GCF of 28 and 49?