This common factor calculator lists every positive integer that divides both numbers you enter. Unlike a GCF tool that returns only the largest shared factor, this page shows the full shared set so you can see every option, not just the maximum.
How to use the common factor calculator
- Enter the first positive integer in field A.
- Enter the second positive integer in field B.
- Read the list of common factors and the GCF shown in the detail output.
How common factors are found
The calculator first finds g = GCF(a, b) with the Euclidean algorithm. Every common factor of a and b must also be a divisor of g. The tool then lists each positive divisor of g from 1 through g. Those values are exactly the common factors of a and b.
Worked example
For 12 and 18, GCF = 6. Divisors of 6 are 1, 2, 3, and 6. Those are the common factors. You can check: 12 and 18 are both divisible by each of those values, and no larger integer divides both.
For 7 and 15 the GCF is 1, so the only common factor is 1. The numbers are coprime.
Common factors vs GCF
Use this page when a lesson asks for all common factors or when you want to pick a shared unit that is not necessarily the largest one. When you only need the greatest shared value for fraction reduction, use the GCF calculator. For multiples, open the LCM calculator. Single-number divisor lists belong on the factor calculator, and prime trees on the prime factorization calculator.
Practical uses
- Choosing a tile, box, or batch size that divides two inventory counts.
- Classroom exercises that ask for the set of common factors, not only the GCF.
- Checking whether two lengths share a measuring unit of 1, 2, 3, or more units.
Limitations
Only positive integers are supported. The list can grow long when the GCF is large, because every divisor of the GCF appears. This tool does not handle three or more inputs at once; reduce pairwise or use the GCF calculator for a three-number greatest factor.
Frequently asked questions
Is 1 always a common factor?
Yes for positive integers. Every integer is divisible by 1, so 1 always appears in the list.
Why does the output also show GCF?
The GCF is the largest value in the common factor list. Showing it helps confirm the list is complete and matches a separate GCF check.
Are common factors the same as common multiples?
No. Factors divide the numbers. Multiples are products that the numbers divide into. Use LCM tools for shared multiples.