Q:

What is the GCF of 29 and 85?

Accepted Solution

A:
Solution: The GCF of 29 and 85 is 1 Methods How to find the GCF of 29 and 85 using Prime Factorization One way to find the GCF of 29 and 85 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 29? What are the Factors of 85? Here is the prime factorization of 29: 2 9 1 29^1 2 9 1 And this is the prime factorization of 85: 5 1 × 1 7 1 5^1 × 17^1 5 1 × 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 29 and 85 is 1. Thus, the GCF of 29 and 85 is: 1 How to Find the GCF of 29 and 85 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 29 and 85 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, 29 and 85: Factors of 29: 1, 29 Factors of 85: 1, 5, 17, 85 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 29 and 85 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 68 and 104? What is the GCF of 38 and 87? What is the GCF of 80 and 77? What is the GCF of 54 and 75? What is the GCF of 60 and 128?