Math Tutor Explains: What is the GCF of 36 and 12?

Need help finding the Greatest Common Factor (GCF)? As your math tutor, when we consider, “What is the GCF of 36 and 12?”, the question we are asking is what would be the largest number that can divide both 36 and 12 exactly, without any remainder left afterwards.

Math Tutor Solution: The GCF of 36 and 12 is 12

Methods

How to find the GCF of 36 and 12 using Prime Factorization

One way to find the GCF of 36 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:

Here is the prime factorization of 36:

22×322^2 × 3^2

And this is the prime factorization of 12:

22×312^2 × 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 36 and 12 by multiplying all the matching prime factors to get a GCF of 36 and 12 as 36:

Thus, the GCF of 36 and 12 is: 36

How to Find the GCF of 36 and 12 by Listing All Common Factors

The first step to this method of finding the Greatest Common Factor of 36 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, 36 and 12:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

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, 4, 6, 12. Since 12 is the largest of these common factors, the GCF of 36 and 12 would be 12.

Math Tutor Suggests: Find the GCF of Other Number Pairs

Want more practice? Try some of these other GCF problems walkthrough from math tutors:

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?

A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.

Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.

Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!

Start 7-Day Free Trial