What is a common factor?

A common factor of two or more numbers is a whole number that divides each of them with no remainder. For 12 and 18, the common factors are 1, 2, 3, and 6.

What is the greatest common factor (GCF)?

The GCF (also called GCD) is the largest of the common factors — for 12 and 18 it is 6. It is the key number for simplifying fractions and splitting quantities into the largest possible equal groups.

How do I find the GCF?

For small numbers, list each number's factors and pick the largest shared one, or compare prime factorizations and multiply the shared primes. For large numbers, the Euclidean algorithm is fastest: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero.

What is the difference between GCF and LCM?

The GCF is the largest number that divides both values; the LCM (least common multiple) is the smallest number both values divide into. They are linked by GCF(a, b) × LCM(a, b) = a × b, so knowing one gives you the other.

Where are common factors used in practice?

Reducing fractions to lowest terms (divide top and bottom by the GCF), dividing items into equal groups, finding common denominators via the LCM, and simplifying ratios in recipes, gears, and scale models.

Common Factor Calculator

Find common factors between two or more numbers. Free, fast, accurate — no signup, mobile-friendly, works in any browser

Number Input

Numbers (comma-separated)

Enter positive integers separated by commas (up to 10 numbers)

What to calculate?

Options

Show calculation steps

Include prime factorization

Quick Reference

GCD: Largest number that divides all input numbers

LCM: Smallest number that all input numbers divide into

Property: For two numbers a, b: GCD(a,b) × LCM(a,b) = a × b

Coprime: Two numbers are coprime if GCD = 1

Numbers: 12, 18

Greatest Common Divisor (GCD)

Largest common factor

Least Common Multiple (LCM)

Smallest common multiple

Relationship Verification

GCD × LCM = 6 × 36 = 216

Product of numbers = 12 × 18 = 216

GCD × LCM = Product of numbers (fundamental relationship)

Prime Factorizations

12 =2^2 × 3

18 =2 × 3^2

All Factors

Factors of 12:

1, 2, 3, 4, 6, 12

Factors of 18:

1, 2, 3, 6, 9, 18

How it works

This calculator finds the factors two or more numbers share, and the greatest of them (the GCD or greatest common factor). The GCD is the largest number that divides all of them evenly — handy for simplifying fractions and ratios.

Greatest common divisor

GCD = largest number that divides every value with no remainder

a, b: the numbers to compare
GCD: greatest common factor

Worked example

Find the GCD of 12 and 18

Factors of 12: 1,2,3,4,6,12
Factors of 18: 1,2,3,6,9,18
Shared: 1,2,3,6

GCD = 6.

Good to know

Dividing a fraction's top and bottom by their GCD reduces it to lowest terms in one step.
The Euclidean algorithm finds the GCD fast without listing all factors.
If the GCD is 1, the numbers are coprime (share no factor but 1).