Q:

What is the GCF of 48 and 112?

Accepted Solution

A:
Solution: The GCF of 48 and 112 is 16 Methods How to find the GCF of 48 and 112 using Prime Factorization One way to find the GCF of 48 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 48? What are the Factors of 112? Here is the prime factorization of 48: 2 4 × 3 1 2^4 × 3^1 2 4 × 3 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 48 and 112 by multiplying all the matching prime factors to get a GCF of 48 and 112 as 4: Thus, the GCF of 48 and 112 is: 4 How to Find the GCF of 48 and 112 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 48 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, 48 and 112: Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 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 48 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 63 and 144? What is the GCF of 32 and 64? What is the GCF of 130 and 128? What is the GCF of 120 and 117? What is the GCF of 112 and 52?