Common Factors Calculator
Find every common factor shared by a list of whole numbers, plus the GCF, with a step-by-step divisor list for each value and their overlap.
How to use this calculator
Type two or more positive whole numbers — separated by spaces or commas — into the box. The calculator lists every divisor of each number, intersects those lists, and reports the common factors together with the GCF (the largest one).
What is a common factor?
A common factor of a set of numbers is a whole number that divides every number in the set with no remainder. Finding them is a three-step process:
- List the factors (divisors) of each number, found by trial division.
- Take the intersection of those lists — the factors that appear in all of them.
- The largest number in that intersection is the GCF (greatest common factor).
Worked example — 16, 24, 64, 136
| Number | Factors |
|---|---|
| 16 | 1, 2, 4, 8, 16 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 64 | 1, 2, 4, 8, 16, 32, 64 |
| 136 | 1, 2, 4, 8, 17, 34, 68, 136 |
Every one of these four lists contains 1, 2, 4, and 8 — no other value repeats across all four. So the common factors are 1, 2, 4, 8, and the GCF is 8.
Second example — 27, 54, 81
| Number | Factors |
|---|---|
| 27 | 1, 3, 9, 27 |
| 54 | 1, 2, 3, 6, 9, 18, 27, 54 |
| 81 | 1, 3, 9, 27, 81 |
The shared entries are 1, 3, 9, and 27, so the common factors are 1, 3, 9, 27 and the GCF is 27.
Common Factors vs. GCF
These two tools answer related questions with different amounts of detail:
| Common Factors | GCF | |
|---|---|---|
| Returns | the whole shared set | only the largest shared value |
| Example (16, 24, 64, 136) | 1, 2, 4, 8 | 8 |
| Use it when | you need every shared divisor, e.g. to split groups evenly in more than one way | you only need the single biggest common divisor, e.g. to reduce a fraction |
Limits
Enter 2 to 10 numbers, each a positive integer no larger than 1,000,000. Both limits keep the trial-division search — which lists every divisor of every number — fast enough to recompute on each keystroke.
Frequently asked questions
- What are the common factors of 16, 24, 64, and 136?
- 1, 2, 4, and 8. Listing each number's divisors — 16: 1, 2, 4, 8, 16; 24: 1, 2, 3, 4, 6, 8, 12, 24; 64: 1, 2, 4, 8, 16, 32, 64; 136: 1, 2, 4, 8, 17, 34, 68, 136 — and keeping only the entries every list shares gives {1, 2, 4, 8}, so the GCF is 8.
- What is a common factor?
- A common factor of a set of numbers is a whole number that divides every one of them with no remainder. It is the intersection of each number's own divisor list — every value in that intersection divides all the given numbers.
- How is Common Factors different from GCF?
- GCF (greatest common factor) returns a single number — the largest common factor. Common Factors returns the whole shared set. For 12 and 18 the GCF is 6, but the full set of common factors is 1, 2, 3, and 6 — GCF is just the biggest member of that set.
- Why does the calculator limit input to 2-10 numbers of at most 1,000,000 each?
- Each number's divisor list is built by trial division, which needs to stay fast on every keystroke. Ten values at up to a million keeps every list — and their overlap — instant to compute and short enough to read.
- Do the common factors always include 1?
- Yes. The number 1 divides every whole number, so it is a common factor of any list you enter, and the GCF is always at least 1.
- What if the numbers share no factor larger than 1?
- Then the only common factor is 1 and the numbers are called coprime (relatively prime) as a set — for example 7 and 13 share nothing but 1.