Q:

What is the GCF of 144 and 28?

Accepted Solution

A:
Solution: The GCF of 144 and 28 is 4 Methods How to find the GCF of 144 and 28 using Prime Factorization One way to find the GCF of 144 and 28 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 28? 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 28: 2 2 × 7 1 2^2 × 7^1 2 2 × 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 144 and 28 by multiplying all the matching prime factors to get a GCF of 144 and 28 as 4: Thus, the GCF of 144 and 28 is: 4 How to Find the GCF of 144 and 28 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 144 and 28 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 28: Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 28: 1, 2, 4, 7, 14, 28 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 144 and 28 would be 4. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 131 and 9? What is the GCF of 63 and 46? What is the GCF of 125 and 38? What is the GCF of 135 and 98? What is the GCF of 10 and 75?