Q:

What is the GCF of 144 and 76?

Accepted Solution

A:
Solution: The GCF of 144 and 76 is 4 Methods How to find the GCF of 144 and 76 using Prime Factorization One way to find the GCF of 144 and 76 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 76? 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 76: 2 2 × 1 9 1 2^2 × 19^1 2 2 × 1 9 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 76 by multiplying all the matching prime factors to get a GCF of 144 and 76 as 4: Thus, the GCF of 144 and 76 is: 4 How to Find the GCF of 144 and 76 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 144 and 76 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 76: Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 76: 1, 2, 4, 19, 38, 76 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 76 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 10 and 1? What is the GCF of 80 and 39? What is the GCF of 83 and 149? What is the GCF of 113 and 59? What is the GCF of 135 and 54?