Two or more whole numbers usually share several divisors, not just one. The greatest common factor gets most of the attention, but the full set of common factors answers practical questions too: which group sizes work for every item, which fraction simplifications are possible, which tile sizes fit two walls. This calculator lists each number’s factors side by side, highlights the ones they share and explains why the GCF holds the whole answer.
How to use the common factors calculator
- Enter two to ten whole numbers, separated by commas or spaces:
24, 36, 60. - The tape lists the common factors, how many there are and the greatest one.
- Below, each number’s factors appear as chips. Shared factors are blue and the GCF is amber, so you can see the overlap at a glance.
Two ways to find common factors
List and compare
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
In every list: 1, 2, 3, 4, 6, 12
Use the GCF
GCF(24, 36, 60) = 12, and the factors of 12 are 1, 2, 3, 4, 6, 12 — the same list with far less writing. The GCF calculator finds the GCF by three different methods, and for big numbers the Euclidean algorithm gets there fastest.
Counting common factors without listing them
Factor the GCF into primes, add 1 to each exponent and multiply. 12 = 2² × 3, so there are (2+1)(1+1) = 6 common factors. Two numbers can share a surprising number of factors: 720,720 and 1,441,440 have 240 in common.
Using common factors in real problems
Equal groups
A teacher has 24 pencils, 36 erasers and 60 stickers and wants identical goody bags with nothing left over. Every common factor is a possible number of bags:
| Bags | Pencils each | Erasers each | Stickers each |
|---|---|---|---|
| 2 | 12 | 18 | 30 |
| 3 | 8 | 12 | 20 |
| 4 | 6 | 9 | 15 |
| 6 | 4 | 6 | 10 |
| 12 | 2 | 3 | 5 |
The GCF, 12, is the largest number of bags; the other common factors give the other workable options.
Simplifying fractions in stages
Any common factor of a numerator and denominator can be divided out. For 24/36 you might divide by 2, then 2, then 3 — or by the GCF, 12, in one step to reach 2/3. The simplify fractions calculator always uses the GCF.
Tiles and grids
Square tiles that fit a 24-inch by 36-inch area exactly can have any side length that is a common factor: 1, 2, 3, 4, 6 or 12 inches.
Relatively prime numbers
If 1 is the only common factor, the numbers are relatively prime. That doesn’t require either number to be prime: 8 = 2³ and 15 = 3 × 5 are coprime, as are any two consecutive whole numbers. Coprime pairs matter in fractions (a fraction is in lowest terms when its numerator and denominator are coprime) and in cryptography.
For a single number’s factors and factor pairs, use the factors calculator. For the opposite idea — numbers that all of yours divide into — use the LCM calculator.
Frequently asked questions
What are common factors?
Numbers that divide each of two or more numbers exactly. The common factors of 24, 36 and 60 are 1, 2, 3, 4, 6 and 12.
How do I find common factors?
List the factors of each number and keep the ones that appear in every list. A faster way is to find the greatest common factor and list its factors — they are exactly the common factors.
Why are the common factors the same as the factors of the GCF?
Any number that divides all of the numbers also divides their greatest common factor, and every factor of the GCF divides all of the numbers. So the two lists are identical. For 24, 36 and 60, the GCF is 12, and the factors of 12 are 1, 2, 3, 4, 6 and 12.
What if the only common factor is 1?
Then the numbers are called relatively prime or coprime. 8 and 15 are an example: they share no factor other than 1, even though neither is prime.
What is the difference between common factors and common multiples?
Common factors divide into every number, so there are only finitely many and the largest is the GCF. Common multiples are numbers every number divides into; there are infinitely many, and the smallest is the LCM.