Q:

What is the GCF of 25 and 74?

Accepted Solution

A:
Solution: The GCF of 25 and 74 is 1 Methods How to find the GCF of 25 and 74 using Prime Factorization One way to find the GCF of 25 and 74 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 74? Here is the prime factorization of 25: 5 2 5^2 5 2 And this is the prime factorization of 74: 2 1 × 3 7 1 2^1 × 37^1 2 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 25 and 74 is 1. Thus, the GCF of 25 and 74 is: 1 How to Find the GCF of 25 and 74 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 25 and 74 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 74: Factors of 25: 1, 5, 25 Factors of 74: 1, 2, 37, 74 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 74 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 40 and 125? What is the GCF of 27 and 150? What is the GCF of 80 and 113? What is the GCF of 36 and 132? What is the GCF of 134 and 111?