Q:

What is the GCF of 85 and 68?

Accepted Solution

A:
Solution: The GCF of 85 and 68 is 17 Methods How to find the GCF of 85 and 68 using Prime Factorization One way to find the GCF of 85 and 68 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 68? 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 68: 2 2 × 1 7 1 2^2 × 17^1 2 2 × 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 68 by multiplying all the matching prime factors to get a GCF of 85 and 68 as 289: Thus, the GCF of 85 and 68 is: 289 How to Find the GCF of 85 and 68 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 85 and 68 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 68: Factors of 85: 1, 5, 17, 85 Factors of 68: 1, 2, 4, 17, 34, 68 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 68 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 99 and 52? What is the GCF of 67 and 90? What is the GCF of 97 and 10? What is the GCF of 22 and 77? What is the GCF of 61 and 34?