Q:

What is the GCF of 85 and 119?

Accepted Solution

A:
Solution: The GCF of 85 and 119 is 17 Methods How to find the GCF of 85 and 119 using Prime Factorization One way to find the GCF of 85 and 119 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 119? 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 119: 7 1 × 1 7 1 7^1 × 17^1 7 1 × 1 7 1 When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 85 and 119 by multiplying all the matching prime factors to get a GCF of 85 and 119 as 289: Thus, the GCF of 85 and 119 is: 289 How to Find the GCF of 85 and 119 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 85 and 119 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 119: Factors of 85: 1, 5, 17, 85 Factors of 119: 1, 7, 17, 119 When you compare the two lists of factors, you can see that the common factor(s) are 1, 17. Since 17 is the largest of these common factors, the GCF of 85 and 119 would be 17. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 16 and 82? What is the GCF of 48 and 13? What is the GCF of 141 and 15? What is the GCF of 83 and 42? What is the GCF of 106 and 11?