Q:

What is the GCF of 104 and 132?

Accepted Solution

A:
Solution: The GCF of 104 and 132 is 4MethodsHow to find the GCF of 104 and 132 using Prime FactorizationOne way to find the GCF of 104 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 104?What are the Factors of 132?Here is the prime factorization of 104:23×1312^3 × 13^123×131And this is the prime factorization of 132:22×31×1112^2 × 3^1 × 11^122×31×111When 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 104 and 132 by multiplying all the matching prime factors to get a GCF of 104 and 132 as 4:Thus, the GCF of 104 and 132 is: 4How to Find the GCF of 104 and 132 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 104 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, 104 and 132:Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104Factors of 132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132When 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 104 and 132 would be 4.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 11 and 3?What is the GCF of 43 and 50?What is the GCF of 99 and 19?What is the GCF of 9 and 134?What is the GCF of 141 and 78?