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.

Teaching Divisibility Rules

Do you teach divisibility rules in your middle school math classes? I’ve always enjoyed teaching divisibility rules, and my 6th grade math students have always seemed to have fun using them!

I’ve read different opinions about whether or not teaching divisibility rules should be a focus in math class, because they may be viewed as ‘tricks.’ I do not view them as tricks, but as a way to develop relationships between numbers.

I think understanding and using divisibility rules in middle school helps students develop number sense and number fluency.

Rather than being taught as a unit, I think divisibility rules should be introduced and then referred to again and again in any applicable situation throughout the year. 

To make the continuous revisiting easier for students, I’ve always liked to have a resource for them to refer to throughout the year. We used to create fold-it-ups, but then I moved to using a Doodle Notes resource or a Math Wheel.

Any reference sheet is helpful so that when you ask a divisibility question, students can grab it (or look at it on a wall) to quickly refresh their memories, if needed.

Where Can Students Apply Divisibility Rules?

There are several math concepts where applying divisibility rules will help students:

1) Working with division facts that are beyond the ‘basics’ 

• Example: 51 divided by 3 
• Students so often believe 51 is prime, but if they take a second to test the rule for 3, they can quickly see that 51 is in fact a composite number.

2) Prime factorization

• When determining the prime factorization of a number like 51, 57 or 87, using the divisibility rules can be very helpful.

3) GCF

• To find GCF, students need to determine what each number can be divided by, so the divisibility rules are quite helpful here.

4) FACTORING 

• If you teach divisibility rules in elementary school, you might not be thinking of this eventual application. However, the more frequently math students work with divisibility rules, the more their number fluency improves, and the easier factoring will be for them.

Methods for Teaching Divisibility

As I mentioned above, I think divisibility rules are learned and retained most effectively when they are introduced and then referred to on a regular basis.

It’s also helpful when students have a resource to refer to if they need a quick reminder, so my favorite way to teach the rules are to use the Doodle Notes or the Math Wheel. 

See Divisibility Resources

These methods are similar because they both incorporate coloring, doodling, and visual memory triggers. I also love these because they:

1. Increase focus and retention during instruction, by incorporating coloring and doodling (this activates both hemispheres of the brain).
2. Are those year-long resources students can keep in their interactive notebooks.

What Are the Rules?

In case you’re teaching divisibility rules for the first time (or haven’t taught them in a long time), I’ve included the divisibility rules for 2, 3, 4, 5, 6, 9, and 10 in this post.

There are rules for 7 and 8 as well, but I don’t normally teach these, as they’re a bit more complicated and maybe a little less useful.

2: if a number ends in a 0, 2, 4, 6, 8, it is divisible by 2

• Example: the number 358 ends in 8, so 358 is divisible by 2

3: if the sum of the digits in a number is divisible by 3, the number is divisible by 3

• Example: the sum of the digits in the number 4,563 is 18. 18 is divisible by 3, so 4,563 is divisible by 3.

4: if the last 2 digits of a number are divisible by 4, the number is divisible by 4

• Example: in the number 248, the last 2 digits (48) are divisible by 4, so 248 is divisible by 4.

5: if a number ends in 0 or 5, it is divisible by 5

• Example: the number 255 ends in 5, so 255 is divisible by 5

6: if a number is divisible by 2 AND 3, it is divisible by 6

• ​Example: the sum of the digits in 246 is 12. 12 is divisible by 3, so 246 is divisible by 3
• 246 ends in 6, so 246 is divisible by 2
• 246 is divisible by 2 AND 3, so 246 is divisible by 6.

9: if the sum of the digits in a number is divisible by 9, the number is divisible by 9

• Example: the sum of the digits in the number 4,563 is 18. 18 is divisible by 9, so 4,563 is divisible by 9.

10: if a number ends in 0, it is divisible by 10

• Example: the number 4,040 ends in 0, so 4,040 divisible by 10

Note:
Finding the sum for the divisibility rules for 3 and 9 sometimes leads some students to start adding the digits to check for every
number.

I’ve found that the use of visuals with the Doodle Notes or the Math Wheel reduced this tendency, as compared to when we used the fold-it ups. 

 

Want to learn more about using math wheels for notes and practice? Click HERE for all the details.

The post Teaching Divisibility Rules in Middle School Math appeared first on Cognitive Cardio Math.