Q:

What is the GCF of 25 and 7?

Accepted Solution

A:
Solution: The GCF of 25 and 7 is 1 Methods How to find the GCF of 25 and 7 using Prime Factorization One way to find the GCF of 25 and 7 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 25? What are the Factors of 7? Here is the prime factorization of 25: 5 2 5^2 5 2 And this is the prime factorization of 7: 7 1 7^1 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 25 and 7 is 1. Thus, the GCF of 25 and 7 is: 1 How to Find the GCF of 25 and 7 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 25 and 7 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, 25 and 7: Factors of 25: 1, 5, 25 Factors of 7: 1, 7 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 25 and 7 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 51 and 14? What is the GCF of 87 and 8? What is the GCF of 134 and 50? What is the GCF of 65 and 149? What is the GCF of 11 and 150?