3 Ways to Find Greatest Common Factor and Finding GCF Word Problem

Ellie — Tue, 24 Jun 2025 09:22:00 +0000

When you’re teaching the greatest common factor to 6th graders, it helps to have a clear structure and multiple methods at your fingertips. Whether you’re brand new to teaching this concept or just want a more effective way to deliver it, this post has you covered. I’ve pulled together two videos and a helpful classroom resource that will take the guesswork out of introducing and practicing GCF.

Greatest Common Factor Videos With Three Strategies That Work

In this first video, I explain what the greatest common factor actually means. Then, we walk through three go-to strategies to find it. We look at listing factors, using prime factorization, and my favorite, which is the ladder method. I show you how to help your students decide which method is best for the numbers they’re working with. I also weave in divisibility rules and factor trees to give your students extra tools for breaking down numbers. Each strategy builds a deeper understanding of how numbers connect. This helps to make the greatest common factor more than just a vocabulary term. It becomes something your students can use.

3 Ways to Find the Greatest Common Factor

Solving GCF Word Problems

Once your students understand how to find the GCF, it’s time to show them how to apply it. In the second video, I walk through a word problem that requires using GCF. I model how your students can organize their thinking, use a guess-and-check strategy if they feel stuck, and connect the numbers in the problem back to what they already know about factoring. We also solve the problem using the ladder method, allowing your students to see how math shows up in everyday problem-solving. This is a great way to answer the classic “When are we going to use this?” question.

Help Students Choose What Works With These Three GCF Strategies

When it comes to teaching the greatest common factor, it’s not just about memorizing the steps. It’s about helping your students understand why each method works and when to use it. Let’s take a closer look at the three strategies highlighted in the video and resource.

Listing Factors is a solid place to start with smaller numbers. You should always encourage your students to list pairs in order (starting with 1 and the number itself) and to stop once they meet in the middle. It’s simple and visual, but it can be tricky when working with larger numbers, especially if your students don’t know all their math facts.

Prime Factorization takes things a step further by using factor trees to break numbers into their prime parts. This method gives your students a way to actually see how numbers are built. They learn how to find what factors two numbers have in common. It’s a great strategy for reinforcing prime numbers and multiplication facts, too.

The Ladder Method is typically students’ favorite! It feels less messy than factor trees and works well with large numbers. You pull out common factors on the side and divide both numbers until there’s nothing left to pull out. It’s straightforward, systematic, and pairs beautifully with visual learning styles. Plus, once your students master it, it becomes their go-to method for both GCF and least common multiple later on.

Greatest Common Factor Resource

To go along with the videos, I’ve created a classroom resource packed with everything you need to teach the greatest common factor from start to finish. The resource includes print and digital versions of GCF notes and practice pages, plus two exit tickets that help you assess understanding right away. Each strategy, listing factors, prime factorization, and the ladder method, has its own dedicated lesson page and step-by-step examples.

Your students can also get a chance to try each method on their own with guided support. There’s a Fold It Up activity that helps solidify how to use GCF and when to apply it. Whether you’re teaching a whole group, a small group, or assigning it digitally, this set is built for flexibility and clarity. Your students will walk away knowing how to find the GCF and why it matters.

Help Students Master the Greatest Common Factor

Teaching the greatest common factor in 6th grade math doesn’t have to be complicated. With the right mix of visuals, guided examples, real-life application, and supportive practice, your students can truly understand and use GCF consistently. Whether you start with the videos, the printables, or both, you’ll set them up for success in future algebraic thinking and number sense.

Save for Later

Remember to save this post to your favorite math Pinterest board for quick access to these greatest common factor resources!

The post 3 Ways to Find Greatest Common Factor and Finding GCF Word Problem appeared first on Cognitive Cardio Math.

How to Find GCF and Spending Time in Middle School Math

laine — Thu, 04 Nov 2021 11:00:00 +0000

GCF (greatest common factor) and spending ‘too much time’ on math topics. These are the middle school math ideas I’m thinking about today.

There were times during the school year when I’d think I had spend too much time on a math topic….not because the kids seemed bored with it or anything like that, but because I had to get so many concepts covered that I was afraid I’d run out of time (I’m sure you know the feeling!).
So, spending more time than I was “supposed to” occasionally stressed me out. But most of the time, I was glad I spent so much time on some concepts, even though I appeared to be “behind” when talking with other teachers about where we were in the curriculum.

When I say that I spent more time, it’s not that I made the students do worksheet after worksheet; instead, we’d practice/interact with the same skills in several different ways.

For example, before a holiday break one year, we worked on finding GCF (greatest common factor). Prior to 6th grade, most of the students had only been taught one method to find GCF: listing out the factors.

When I taught GCF, I also taught students the prime factorization method and the ladder method (you may already know that I LOVE the ladder method, for most sets of numbers:-).

So, we worked on finding GCF, and then we had the holiday break.

Day 1 of Reviewing How to Find GCF

On our first day back, we briefly reviewed the methods and then I had the students:
1) Partner up (using the equivalent expressions partnering cards for extra reinforcement of that concept!) and
2) Write short paragraphs to explain each method (and include their own examples).

That activity took most of the math class (after our warm up and reviewing….only a 40 minute class).

Day 2 of Reviewing How to Find GCF

The following day, with the same partners, the students started their GCF Footloose task cards. The task cards required students to:

list factors
find GCF of given numbers
solve quite a few GCF word problems

The students in the first class period didn’t even get half-way through the task cards, and I started thinking, “Oh, no, now we have to use another day to finish this tomorrow…or maybe we shouldn’t finish, we should just move on.”

BUT, as I listened to my students’ discussions, class after class, I decided that we definitely needed to finish the next day.
And I definitely needed to continue to spend the same amount of time on topics that I had been spending, in all the different ways I employed, because what I heard from observing students confirmed that spending this time is what’s best for them. I heard:

Quality math discussions
Students giving math advice to each other
Students finding factors of larger numbers by testing divisibility rules (without me advising them to!)
Students using different methods to confirm answers

Students helping one another by pointing out one another’s mistakes (politely) – which means they can identify mistakes in work!

I was so impressed with several things I observed during these days:

Students’ ability to communicate about how to complete a problem
Students’ ability to communicate disagreement with a partner
Students turning to each other for help and truly trying to figure out the answer before asking me
An increased use of math language!

I loved to walk around and listen to my students. I had my students work in partners and groups quite often throughout our studies of various math topics, and their discussions continually improved throughout the year, as did their collaborative thinking skills.

Was the extra time I spent on GCF and other math topics worth it? Absolutely!

GCF Task Cards

To check out the Greatest Common Factor task cards, which has 2 sets of cards, for differentiation purposes, click the link below.
GCF & Factors Footloose Task Cards

The post How to Find GCF and Spending Time in Middle School Math appeared first on Cognitive Cardio Math.

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