Q:

What is the GCF of 73 and 75?

Accepted Solution

A:
Solution: The GCF of 73 and 75 is 1 Methods How to find the GCF of 73 and 75 using Prime Factorization One way to find the GCF of 73 and 75 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 73? What are the Factors of 75? Here is the prime factorization of 73: 7 3 1 73^1 7 3 1 And this is the prime factorization of 75: 3 1 × 5 2 3^1 × 5^2 3 1 × 5 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 73 and 75 is 1. Thus, the GCF of 73 and 75 is: 1 How to Find the GCF of 73 and 75 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 73 and 75 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, 73 and 75: Factors of 73: 1, 73 Factors of 75: 1, 3, 5, 15, 25, 75 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 73 and 75 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 94 and 146? What is the GCF of 25 and 68? What is the GCF of 50 and 10? What is the GCF of 58 and 21? What is the GCF of 103 and 37?