Q:

What is the GCF of 108 and 36?

Accepted Solution

A:
Solution: The GCF of 108 and 36 is 36 Methods How to find the GCF of 108 and 36 using Prime Factorization One way to find the GCF of 108 and 36 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 108? What are the Factors of 36? Here is the prime factorization of 108: 2 2 × 3 3 2^2 × 3^3 2 2 × 3 3 And this is the prime factorization of 36: 2 2 × 3 2 2^2 × 3^2 2 2 × 3 2 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 108 and 36 by multiplying all the matching prime factors to get a GCF of 108 and 36 as 36: Thus, the GCF of 108 and 36 is: 36 How to Find the GCF of 108 and 36 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 108 and 36 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, 108 and 36: Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 4, 6, 9, 12, 18, 36. Since 36 is the largest of these common factors, the GCF of 108 and 36 would be 36. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 48 and 142? What is the GCF of 141 and 41? What is the GCF of 96 and 75? What is the GCF of 31 and 8? What is the GCF of 74 and 66?