Common Factors Calculator
Separate multiple numbers with commas
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Use our Common Factors Calculator to quickly find all common factors shared by two or more numbers. Simply enter your numbers separated by commas, click Calculate, and instantly see the complete list of factors for each number along with the Greatest Common Factor (GCF).
Whether you’re solving math homework, simplifying fractions, studying number theory, or checking divisibility, this calculator provides fast and accurate results.
What Are Common Factors?
A factor is a number that divides another number evenly without leaving a remainder. Common factors are the numbers that divide two or more integers exactly.
For example, Consider the factors of 24, 36, and 60:
| Number | Factors |
|---|---|
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |
The factors shared by all three numbers are:
1, 2, 3, 4, 6, and 12
Since all three numbers can be divided evenly by these values, they are called the common factors.
The largest common factor is 12, so:
GCF (24, 36, 60) = 12
These are known as the common factors because they divide each number evenly.
What Is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), is the largest factor that all numbers in a set share.
In the example above:
GCF (27, 54, 81) = 27
Since 27 is the largest number that divides all three values without a remainder, it is the greatest common factor.
How to Use the Common Factors Calculator
- Enter two or more positive integers.
- Separate each number with a comma.
- Click the Calculate button.
- View:
- All factors of each number
- Common factors shared by all numbers
- The Greatest Common Factor (GCF)
The calculator performs the calculations instantly and displays easy-to-understand results.
Example Calculation
Find the common factors of 12, 18, and 24.
Factors of Each Number
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 8, 12, 24
Common Factors
1, 2, 3, 6
Greatest Common Factor
GCF = 6
Why Find Common Factors?
Finding common factors is useful for:
- Simplifying fractions
- Solving algebra problems
- Understanding divisibility rules
- Finding equivalent ratios
- Working with least common multiples (LCM)
- Improving number sense and math skills
Students, teachers, and professionals frequently use common factor calculations in mathematics and everyday problem-solving.
Frequently Asked Questions
What is a common factor?
A common factor is a number that divides two or more numbers exactly without leaving a remainder.
What is the difference between a factor and a common factor?
A factor belongs to one number, while a common factor belongs to two or more numbers.
Is GCF the same as GCD?
Yes. Greatest Common Factor (GCF) and Greatest Common Divisor (GCD) refer to the same mathematical concept.
Can a calculator find factors of large numbers?
Yes. Our calculator can quickly identify factors, common factors, and the greatest common factor for both small and large integers.
What is the common factor of all numbers?
The number 1 is a common factor of every positive integer.