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List every common factor shared by a set of integers and instantly spot the greatest common factor.
Example
For the numbers 12, 18 and 24:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 3, 6
GCF: 6
The common factors are exactly the divisors of the GCF (6).
How it works
Enter two or more whole numbers separated by commas, spaces or new lines. The tool computes the GCF, then lists all divisors of that GCF — these are exactly the common factors.
Good to know
The Common Factor Calculator takes a list of two or more whole numbers and returns every positive integer that divides all of them, while highlighting the largest one — the greatest common factor (GCF). It's handy for students checking homework on factors and divisors, teachers building examples, and anyone who needs to reduce fractions, scale recipes or measurements down to whole units, or split quantities into equal groups without remainders.
You'd reach for it whenever the question is "what sizes divide all of these evenly?" rather than just "what's the single biggest divisor?". For instance, if you want to cut three boards of 12, 18 and 24 units into identical pieces with nothing left over, each common factor (1, 2, 3, 6) is a valid piece length, and the GCF (6) is the longest piece you can cut.
Reading the output is straightforward: the big number is the GCF, "Numbers used" confirms how many of your entries were actually counted, "Common factors" is the count of shared divisors, and the full comma-separated list shows them all in ascending order. The first value is always 1 (every set shares it) and the last value is always the GCF — that ordering is a quick sanity check that the list is complete.
- Tip: the tool drops zeros, decimals and anything non-integer before calculating, and it uses the absolute value of negatives, so -18 and 18 behave identically. If you paste data and the count looks low, scan for stray decimals or blanks. If the GCF comes back as 1, the numbers are coprime and share no factor other than 1.
Frequently asked questions
How are common factors related to the GCF?
Every common factor of a set of numbers divides their greatest common factor, and every divisor of the GCF is a common factor. So once you know the GCF, listing its divisors gives you all common factors.
What happens with negative numbers or zero?
Negative numbers are treated by their absolute value, since factors are positive. Zeros and non-integers are ignored because every number divides zero, which would make the factor list meaningless.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between a common factor and the greatest common factor?
A common factor is any positive integer that divides all the numbers in your set, so a set usually has several. The greatest common factor is simply the largest of those common factors.
How do you find the common factors of two numbers by hand?
List all the divisors of each number, then keep only the values that appear in every list. A faster shortcut is to find the GCF first, since every divisor of the GCF is automatically a common factor of the whole set.
Can you find common factors of three or more numbers at once?
Yes. The shared factors of three or more integers are exactly the divisors common to all of them, which equals the divisors of the GCF of the entire group. This calculator accepts as many integers as you enter.
What are the common factors of 12 and 18?
They are 1, 2, 3 and 6, and the greatest common factor is 6. Every one of these numbers divides both 12 and 18 with no remainder.
When do two numbers have only 1 as a common factor?
When their greatest common factor is 1, the numbers are called coprime or relatively prime, meaning they share no prime factors. For example, 8 and 15 have only 1 in common.
How are common factors used to simplify fractions?
Dividing both the numerator and denominator by a common factor gives an equivalent fraction in smaller terms. Dividing by the greatest common factor reduces the fraction to its lowest terms in a single step.
Does 1 always count as a common factor?
Yes, 1 divides every integer, so it is a common factor of any set of numbers. That is why it always appears first in the results.
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