Q:

What is the GCF of 85 and 21?

Accepted Solution

A:
Solution: The GCF of 85 and 21 is 1 Methods How to find the GCF of 85 and 21 using Prime Factorization One way to find the GCF of 85 and 21 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 85? What are the Factors of 21? Here is the prime factorization of 85: 5 1 × 1 7 1 5^1 × 17^1 5 1 × 1 7 1 And this is the prime factorization of 21: 3 1 × 7 1 3^1 × 7^1 3 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 85 and 21 is 1. Thus, the GCF of 85 and 21 is: 1 How to Find the GCF of 85 and 21 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 85 and 21 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, 85 and 21: Factors of 85: 1, 5, 17, 85 Factors of 21: 1, 3, 7, 21 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 85 and 21 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 59 and 55? What is the GCF of 32 and 130? What is the GCF of 95 and 135? What is the GCF of 100 and 17? What is the GCF of 141 and 77?