Common Factor
Find all common factors of two numbers with this free online calculator. Get instant results, factor lists, and count for any pair of positive or negative integers.
About This Calculator
Our Common Factor Calculator quickly finds all positive integers that divide two numbers exactly. Whether you're solving math problems, simplifying fractions, or studying number theory, this tool shows every common factor along with the total count. It handles positive and negative integers, zero, and co-prime pairs -- all for free.
Common factors are widely used in mathematics: simplifying fractions by dividing numerator and denominator by a common factor, finding the greatest common factor (GCF) from the list, and understanding the relationship between numbers. Unlike a GCF calculator that returns only the largest value, this page gives you the complete set so you can see every divisor both numbers share.
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. For example, 1, 2, 3, and 6 are common factors of 12 and 18 because each divides both 12 and 18 evenly.
How do I use the Common Factor Calculator?
Enter two integers in the input fields above and click Calculate. The calculator will instantly list all positive common factors and display the total count. You can also share results via the generated URL.
What is the difference between a common factor and the greatest common factor (GCF)?
Common factors are all numbers that divide both inputs evenly (e.g., 1, 2, 3, 6 for 12 and 18). The greatest common factor (GCF) is the largest number in that set -- 6 in this example. This calculator lists every common factor, not just the largest.
Can I find common factors for negative numbers?
Yes. The calculator uses the absolute value of each input to find factors, so common factors are always shown as positive integers. For example, -12 and 18 have the same common factors as 12 and 18: 1, 2, 3, and 6.
What are common factors of 0 and another number?
Zero is divisible by every non-zero integer, so the common factors of 0 and any non-zero number N are all the positive factors of N. For example, common factors of 0 and 12 are 1, 2, 3, 4, 6, and 12.
What does it mean if two numbers have no common factors other than 1?
Numbers that share only 1 as a common factor are called co-prime (or relatively prime). For example, 8 and 15 are co-prime because their common factors are just 1. This calculator will show 'None (co-prime)' when the only common factor is 1.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration required.