Q:

What is the GCF of 144 and 48?

Accepted Solution

A:
Solution: The GCF of 144 and 48 is 48 Methods How to find the GCF of 144 and 48 using Prime Factorization One way to find the GCF of 144 and 48 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 144? What are the Factors of 48? Here is the prime factorization of 144: 2 4 × 3 2 2^4 × 3^2 2 4 × 3 2 And this is the prime factorization of 48: 2 4 × 3 1 2^4 × 3^1 2 4 × 3 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 144 and 48 by multiplying all the matching prime factors to get a GCF of 144 and 48 as 36: Thus, the GCF of 144 and 48 is: 36 How to Find the GCF of 144 and 48 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 144 and 48 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, 144 and 48: Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Since 48 is the largest of these common factors, the GCF of 144 and 48 would be 48. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 32 and 102? What is the GCF of 55 and 134? What is the GCF of 148 and 56? What is the GCF of 22 and 11? What is the GCF of 6 and 17?