Find all common factors of two or more numbers instantly. Calculate shared divisors and the greatest common factor (GCF) with step-by-step methods. Free online common factor calculator for simplifying fractions and solving math problems.
Please provide integers separated by a comma "," and click the "Calculate" button to find their common factors.
Let's start simple. A factor is any number that divides evenly into another number. No remainders allowed. So the factors of 12 are 1, 2, 3, 4, 6, and 12. Each of those divides 12 perfectly.
Now, a common factor is just a factor that two numbers share. Like if you're looking at 12 and 18, both numbers can be divided by 1, 2, 3, and 6. Those four numbers are the common factors.
The greatest common factor (GCF) is the biggest one on that list. For 12 and 18, that's 6. It's the largest number that can divide both of them evenly.
Sounds simple, right? It really is once you get the hang of it.
Using our calculator is about as easy as it gets. Here's what you do:
That's it. The calculator will show you:
All the common factors of both numbers
The greatest common factor (GCF)
A step-by-step breakdown
Let's try an example. Say you want to find the common factors of 24 and 36. Type those in, and you'll see the common factors are 1, 2, 3, 4, 6, and 12. The GCF is 12.
You won't always have a calculator handy. Maybe it's a test, or maybe you just want to understand the process. Either way, here's how to do it manually.
This is the most straightforward method. Just list every factor of each number, then find what they share.
Example: Find the common factors of 16 and 24
Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4, 8
GCF: 8
This method works great for smaller numbers. But for bigger numbers, it can take a while.
This method is a bit more advanced, but it's super useful for large numbers. You break each number down into its prime factors, then find what they have in common.
Example: Find the GCF of 36 and 48
Prime factors of 36: 2 × 2 × 3 × 3
Prime factors of 48: 2 × 2 × 2 × 2 × 3
Common prime factors: 2 × 2 × 3
GCF: 2 × 2 × 3 = 12
See how that works? You just multiply the common prime factors together.
This one sounds fancy, but it's actually pretty simple. You keep subtracting the smaller number from the larger one until you get to zero. The last non-zero number is the GCF.
Example: Find the GCF of 48 and 18
48 - 18 = 30
30 - 18 = 12
18 - 12 = 6
12 - 6 = 6
6 - 6 = 0
GCF: 6
This method is great for big numbers because it's fast and doesn't require listing all factors.
You might be thinking, "When am I ever going to use this?" More often than you'd think.
Everyone makes mistakes when learning this stuff. Here are the most common ones so you can avoid them.
Forgetting That 1 Is Always a Factor
Every number has 1 as a factor. So 1 is always a common factor of any two numbers. Don't forget to include it.
Confusing Factors With Multiples
This is a big one. Factors divide into a number. Multiples are what you get when you multiply a number. So 3 is a factor of 12, but 12 is a multiple of 3. They're opposites.
Stopping Too Early
When listing factors, people sometimes stop before they find all of them. For example, the factors of 24 include 12 and 24, not just 1, 2, 3, 4, 6, and 8. Make sure you check all the way up to the number itself.
Not Checking All Common Factors
Just because you found one common factor doesn't mean it's the greatest. Always check if there's a bigger one. For 12 and 18, 3 is a common factor, but 6 is greater.
What if you need to find the common factors of three numbers? The process is the same, just with more numbers.
Example: Find the common factors of 12, 18, and 24
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 6
GCF: 6
Our calculator can handle this too. Just enter the numbers one at a time.
This is a subtle but important difference. Common factors are all the factors that two numbers share. The greatest common factor is the largest one.
Common Factors
All the factors that two numbers share
Greatest Common Factor
The largest one on the list
Think of it like this. If you're looking at a group of friends, the common factors are all the things they have in common. The greatest common factor is the most important thing they share. For most math problems, you'll need the GCF. But sometimes, you just need to know all the common factors.
Common factors aren't just a math class thing. They show up everywhere in real life. From splitting bills to measuring ingredients for a recipe, understanding common factors makes life easier.
Plus, it's a foundational skill for more advanced math. Once you master common factors, things like algebra and number theory become much more approachable.
So whether you're a student cramming for a test, a parent helping with homework, or just someone who wants to understand math better, our common factor calculator is here to help.
A factor divides evenly into a number. A multiple is what you get when you multiply a number by another number. So 3 is a factor of 12 because 3 × 4 = 12. But 12 is a multiple of 3 because 3 × 4 = 12. They're two sides of the same coin.
For large numbers, use the prime factorization method or the Euclidean algorithm. Break each number into its prime factors, then multiply the common ones. Or keep subtracting the smaller number from the larger one until you get to zero. The last non-zero number is the GCF.
Yes. Every number has 1 as a factor, so 1 is always a common factor of any two numbers. Don't forget to include it when listing common factors.
The common factors of 12 and 18 are 1, 2, 3, and 6. The greatest common factor is 6.
Just type in two numbers and hit calculate. The calculator will show you all the common factors and the greatest one. It's that simple.
Yes. The process is the same as for two numbers. List all factors of each number, then find what they all share. Our calculator can handle three or more numbers.
Common factors are used in simplifying fractions, splitting things evenly, and solving real-world problems. They're also a foundation for more advanced math like algebra.
GCF stands for greatest common factor, which is the largest number that divides two numbers evenly. LCM stands for least common multiple, which is the smallest number that both numbers divide into. They're related but different concepts.
Find the GCF of the numerator and denominator. Then divide both by that number. For example, to simplify 24/36, find the GCF of 24 and 36, which is 12. Then divide both by 12 to get 2/3.
The most common mistake is forgetting that 1 is always a factor. Another is confusing factors with multiples. And some people stop listing factors too early, missing some of them.
You can list all factors of each number, use prime factorization, or use the Euclidean algorithm. All three methods work well for different situations.
The common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12. The greatest common factor is 12.