Common Factor Calculator
List every factor shared by two or more numbers — not just the greatest common factor — with each number's own full factor list shown alongside for comparison.
Common Factors
1, 2, 3, 6
Greatest Common Factor
6
Result
The common factors of 12, 18, 24 are: 1, 2, 3, 6. The greatest of these (the GCF) is 6.
Every common factor, smallest to largest
What is a Common Factor Calculator?
A factor of a number is any positive integer that divides it evenly, with no remainder — 12 has the factors 1, 2, 3, 4, 6, and 12. A common factor is a factor shared by two or more numbers at once. This calculator lists every common factor across all the numbers you enter, not just the single largest one.
This is deliberately a different tool than a plain GCF Calculator, which only returns the greatest common factor. Seeing the complete list matters whenever you need every valid shared divisor — for example, finding every group size that divides a set of quantities evenly, not just the largest possible one.
Full Factor List for Each Number
Every factor of each input number, with the shared (common) ones highlighted — this is what the calculator actually compares to find the common factors above.
| Number | Factors |
|---|---|
| 12 |
1
2
3
4
6
12
|
| 18 |
1
2
3
6
9
18
|
| 24 |
1
2
3
4
6
8
12
24
|
How Common Factors Are Found
Every common factor of a set of numbers is also a factor of their greatest common factor (GCF) — so instead of comparing each number's complete factor list directly, this calculator first computes the GCF using the Euclidean algorithm, then lists every divisor of that GCF. That shortcut works because the GCF itself is built entirely out of the factors the numbers have in common, so nothing outside the GCF's own divisors could possibly be shared by all of them.
Common Factors vs. the Greatest Common Factor
The GCF is just one number — the single largest common factor. The full common-factor list includes every number that divides all the inputs evenly, including 1 (which is always a common factor of any set of whole numbers) and every other shared divisor in between. For 12, 18, and 24, the GCF is 6, but the complete common factor list is 1, 2, 3, and 6.
Why the Full List Matters
Sometimes the greatest common factor isn't actually the useful answer. If you're splitting 12 apples, 18 oranges, and 24 bananas into identical fruit baskets, the GCF (6) tells you the maximum number of baskets you can make with no fruit left over — but if you specifically wanted exactly 3 baskets instead, you'd need to know that 3 is also a valid common factor, which a GCF-only calculator wouldn't surface directly.
A Note on Very Large Numbers
Listing every factor of a number gets computationally expensive as the number grows into the billions or beyond. This calculator lists divisors efficiently by enumerating the (usually much smaller) GCF's divisors rather than the original numbers' — but if the GCF itself is extremely large, the full list is omitted in favor of showing just 1 and the GCF, to keep the page responsive.
Example — Your Current Inputs
The common factors of 12, 18, 24 are: 1, 2, 3, 6. The greatest of these (the GCF) is 6.
Additional Example — Splitting Classroom Supplies
A teacher has 20 pencils, 30 erasers, and 40 stickers to split evenly among identical goodie bags. The common factors of 20, 30, and 40 are 1, 2, 5, and 10 — so the teacher could make 2, 5, or 10 identical bags with nothing left over, but not any other number of bags (like 3 or 4), since those aren't common factors of all three quantities.
Frequently Asked Questions
Is 1 always a common factor?
Yes — 1 divides every whole number evenly, so it's a common factor of any set of positive integers, even if they share no other factors (in which case they're called "coprime" or "relatively prime").
What's the difference between this and the GCF Calculator?
The GCF Calculator returns only the single greatest common factor. This calculator lists every common factor, including 1, the GCF, and everything shared in between.
Can common factors be negative?
Mathematically, negative divisors exist too, but this calculator (like most factor tools) only considers positive whole numbers, since that's what almost every real-world use case — splitting quantities, simplifying fractions, scheduling — calls for.
Does this work for more than two numbers at once?
Yes — enter any number of values separated by commas or spaces, and the calculator finds the factors common to all of them simultaneously, the same way it would for just two.