Q:

What is the GCF of 80 and 112?

Accepted Solution

A:
Solution: The GCF of 80 and 112 is 16 Methods How to find the GCF of 80 and 112 using Prime Factorization One way to find the GCF of 80 and 112 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 80? What are the Factors of 112? Here is the prime factorization of 80: 2 4 × 5 1 2^4 × 5^1 2 4 × 5 1 And this is the prime factorization of 112: 2 4 × 7 1 2^4 × 7^1 2 4 × 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 80 and 112 by multiplying all the matching prime factors to get a GCF of 80 and 112 as 4: Thus, the GCF of 80 and 112 is: 4 How to Find the GCF of 80 and 112 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 80 and 112 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, 80 and 112: Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8, 16. Since 16 is the largest of these common factors, the GCF of 80 and 112 would be 16. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 9 and 48? What is the GCF of 99 and 28? What is the GCF of 33 and 143? What is the GCF of 75 and 16? What is the GCF of 95 and 50?