Q:

What is the GCF of 88 and 132?

Accepted Solution

A:
Solution: The GCF of 88 and 132 is 44 Methods How to find the GCF of 88 and 132 using Prime Factorization One way to find the GCF of 88 and 132 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 88? What are the Factors of 132? Here is the prime factorization of 88: 2 3 × 1 1 1 2^3 × 11^1 2 3 × 1 1 1 And this is the prime factorization of 132: 2 2 × 3 1 × 1 1 1 2^2 × 3^1 × 11^1 2 2 × 3 1 × 1 1 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 88 and 132 by multiplying all the matching prime factors to get a GCF of 88 and 132 as 484: Thus, the GCF of 88 and 132 is: 484 How to Find the GCF of 88 and 132 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 88 and 132 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, 88 and 132: Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88 Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 11, 22, 44. Since 44 is the largest of these common factors, the GCF of 88 and 132 would be 44. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 66 and 57? What is the GCF of 108 and 25? What is the GCF of 99 and 23? What is the GCF of 83 and 122? What is the GCF of 43 and 125?