Q:

What is the GCF of 17 and 147?

Accepted Solution

A:
Solution: The GCF of 17 and 147 is 1 Methods How to find the GCF of 17 and 147 using Prime Factorization One way to find the GCF of 17 and 147 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 17? What are the Factors of 147? Here is the prime factorization of 17: 1 7 1 17^1 1 7 1 And this is the prime factorization of 147: 3 1 × 7 2 3^1 × 7^2 3 1 × 7 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 17 and 147 is 1. Thus, the GCF of 17 and 147 is: 1 How to Find the GCF of 17 and 147 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 17 and 147 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, 17 and 147: Factors of 17: 1, 17 Factors of 147: 1, 3, 7, 21, 49, 147 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 17 and 147 is 1. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 35 and 9? What is the GCF of 93 and 4? What is the GCF of 33 and 116? What is the GCF of 89 and 107? What is the GCF of 75 and 119?