Q:

What is the GCF of 48 and 64?

Accepted Solution

A:
Solution: The GCF of 48 and 64 is 16 Methods How to find the GCF of 48 and 64 using Prime Factorization One way to find the GCF of 48 and 64 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 64? 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 64: 2 6 2^6 2 6 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 64 by multiplying all the matching prime factors to get a GCF of 48 and 64 as 4: Thus, the GCF of 48 and 64 is: 4 How to Find the GCF of 48 and 64 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 48 and 64 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 64: Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 64: 1, 2, 4, 8, 16, 32, 64 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 64 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 23 and 83? What is the GCF of 87 and 50? What is the GCF of 132 and 63? What is the GCF of 15 and 106? What is the GCF of 41 and 131?