Q:

What is the GCF of 28 and 14?

Accepted Solution

A:
Solution: The GCF of 28 and 14 is 14 Methods How to find the GCF of 28 and 14 using Prime Factorization One way to find the GCF of 28 and 14 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 28? What are the Factors of 14? Here is the prime factorization of 28: 2 2 × 7 1 2^2 × 7^1 2 2 × 7 1 And this is the prime factorization of 14: 2 1 × 7 1 2^1 × 7^1 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 28 and 14 by multiplying all the matching prime factors to get a GCF of 28 and 14 as 196: Thus, the GCF of 28 and 14 is: 196 How to Find the GCF of 28 and 14 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 28 and 14 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, 28 and 14: Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 14: 1, 2, 7, 14 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 28 and 14 would be 14. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 137 and 56? What is the GCF of 48 and 47? What is the GCF of 103 and 35? What is the GCF of 53 and 88? What is the GCF of 40 and 136?