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Common Factor Calculator

Enter two or more whole numbers to list every factor they share, find the greatest common factor, and see each number's factors side by side.

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How to use the common factor calculator

  1. Type two or more whole numbers, separated by commas, spaces or new lines. You can enter up to 30, each up to one trillion.
  2. The common factors appear at the top. When there are more than 12, the top shows how many, and the full list sits in a box you can copy.
  3. Read the working to see how the list comes from the greatest common factor.
  4. Compare each number's own factors in the table underneath.

How common factors are found

A common factor divides every number in your list with no remainder. You could list the factors of each number and keep the ones that appear everywhere, but there is a shortcut:

Common factors of a, b, c, … = factors of GCF(a, b, c, …)

Any number that divides all of them must also divide their greatest common factor, and every factor of the GCF divides all of them. So the calculator finds the GCF with Euclid's algorithm, then lists the factors of the GCF by testing divisors up to its square root. This stays fast for large numbers where listing every factor of every number would be slow.

Worked example

The calculator starts with 12, 18 and 30.

  1. Factors of 12: 1, 2, 3, 4, 6, 12.
  2. Factors of 18: 1, 2, 3, 6, 9, 18.
  3. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
  4. The numbers in all three lists are 1, 2, 3 and 6.

Using the shortcut: GCF(12, 18) = 6 and GCF(6, 30) = 6, and the factors of 6 are 1, 2, 3 and 6, the same four numbers. The greatest is 6, so 12, 18 and 30 can all be split into 6 equal groups, but no more.

Reading the result

Result What it means Example
Only 1 The numbers are coprime 8 and 15
1 and a prime The GCF is that prime 14 and 21 share 1 and 7
Many common factors The numbers share several primes 48, 72 and 120 share 8 factors

The count of common factors follows from the GCF's prime factorization. 48, 72 and 120 have a GCF of 24 = 2³ × 3, so they share (3 + 1)(1 + 1) = 8 factors: 1, 2, 3, 4, 6, 8, 12 and 24. For the full breakdown of one number, use the factor calculator or the prime factorization calculator.

Where common factors come up

  • Simplifying fractions. Any common factor of the top and bottom can be cancelled. Cancelling the greatest one, the GCF, gets you to lowest terms in one step.
  • Equal groups. If you have 12 red, 18 blue and 30 green marbles and want identical bags with nothing left over, the number of bags must be a common factor: 1, 2, 3 or 6.
  • Tiling and cutting. A rectangle that is 48 by 72 inches can be covered with square tiles whose side is any common factor of 48 and 72, up to 24 inches.

Frequently asked questions

What is the difference between common factors and the GCF?

The common factors are every number that divides all of yours. The GCF is just the largest of them. Every other common factor divides the GCF, which is why the calculator finds the GCF first.

Is 1 always a common factor?

Yes. 1 divides every whole number, so it is a common factor of any list. When it is the only one, the numbers are called coprime or relatively prime, like 8 and 15.

Why can't I enter 0?

Every whole number divides 0, so including 0 would not change which factors the numbers share. The calculator asks you to leave it out so the result is clear.

How many common factors can numbers have?

As many as their GCF has factors. 720,720 and 1,441,440 have a GCF of 720,720, which has 240 factors, so the two numbers share 240 common factors. The calculator shows the full list in the copy box when there are more than 12.

Related calculators

  • GCF Calculator — Greatest common factor of two or more whole numbers, with Euclid's algorithm and a prime factorization check.
  • Factor Calculator — Every factor and factor pair of a whole number, with the count, the sum and prime, perfect or abundant checks.
  • LCM Calculator — Least common multiple of two or more whole numbers, worked out by prime factorization and by the GCF method.
  • Prime Factorization Calculator — Break a number into prime factors with exponents, see the factor tree, check if it is prime and count its divisors.

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