Q:

What is the GCF of 30 and 12?

Accepted Solution

A:
Solution: The GCF of 30 and 12 is 6 Methods How to find the GCF of 30 and 12 using Prime Factorization One way to find the GCF of 30 and 12 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 30? What are the Factors of 12? Here is the prime factorization of 30: 2 1 × 3 1 × 5 1 2^1 × 3^1 × 5^1 2 1 × 3 1 × 5 1 And this is the prime factorization of 12: 2 2 × 3 1 2^2 × 3^1 2 2 × 3 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 30 and 12 by multiplying all the matching prime factors to get a GCF of 30 and 12 as 36: Thus, the GCF of 30 and 12 is: 36 How to Find the GCF of 30 and 12 by Listing All Common Factors The first step to this method of finding the Greatest Common Factor of 30 and 12 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, 30 and 12: Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 12: 1, 2, 3, 4, 6, 12 When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 3, 6. Since 6 is the largest of these common factors, the GCF of 30 and 12 would be 6. Find the GCF of Other Number Pairs Want more practice? Try some of these other GCF problems: What is the GCF of 44 and 16? What is the GCF of 103 and 134? What is the GCF of 41 and 17? What is the GCF of 100 and 80? What is the GCF of 89 and 69?