Q:

What is the GCF of 68 and 25?

Accepted Solution

A:
Solution: The GCF of 68 and 25 is 1 Methods How to find the GCF of 68 and 25 using Prime Factorization One way to find the GCF of 68 and 25 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 68? What are the Factors of 25? Here is the prime factorization of 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 1 7 1 And this is the prime factorization of 25: 5 2 5^2 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 68 and 25 is 1. Thus, the GCF of 68 and 25 is: 1 How to Find the GCF of 68 and 25 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 68 and 25 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, 68 and 25: Factors of 68: 1, 2, 4, 17, 34, 68 Factors of 25: 1, 5, 25 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 68 and 25 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 20 and 105? What is the GCF of 14 and 81? What is the GCF of 86 and 122? What is the GCF of 23 and 144? What is the GCF of 33 and 135?