Common Factor Calculator
Find all common factors (divisors) of two or more numbers. Instantly see the shared factors and the Greatest Common Factor (GCF).
Separate numbers with commas or spaces.
What are Common Factors?
A factor is a number that divides another number evenly. A common factor is a number that is a factor of two or more numbers.
For example, let's find the common factors of 12 and 18:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
The numbers that appear in both lists are 1, 2, 3, and 6. These are the common factors.
Why calculate common factors?
- Simplifying Fractions: To reduce a fraction to its simplest form, you divide the numerator and denominator by their greatest common factor.
- Distribution: Helps in dividing items into equal-sized groups with nothing left over.
- Algebra: Essential for factoring polynomials and solving equations.
? Frequently Asked Questions
Yes, 1 is a factor of every integer, so it is always a common factor for any set of numbers.
If the only common factor is 1, the numbers are said to be 'relatively prime' or 'coprime'. For example, 8 and 15 share no factors other than 1.
Yes! This calculator accepts lists of multiple numbers. A common factor must divide *every* number in the list evenly.