Guide
What Is the Greatest Common Factor (GCF)?
The greatest common factor is the key to writing any fraction in its simplest form.
The greatest common factor is the key to writing any fraction in its simplest form.
What the GCF is
The greatest common factor (GCF), also called the greatest common divisor, is the largest whole number that divides two or more numbers without a remainder. The GCF of 12 and 18 is 6.
Finding it by listing factors
List the factors of each number and pick the largest they share. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The biggest shared factor is 6.
Finding it by prime factorization
Break each number into primes and multiply the shared ones. 12 = 2 x 2 x 3 and 18 = 2 x 3 x 3; the shared primes are 2 and 3, so the GCF is 2 x 3 = 6.
Why the GCF matters for fractions
To simplify a fraction, you divide the numerator and denominator by their GCF. For 12/18, dividing both by 6 gives 2/3 in one step.
Related tools & guides
Frequently asked
What is the greatest common factor?
The largest whole number that divides two or more numbers evenly. The GCF of 12 and 18 is 6.
How do you find the GCF?
List the factors of each number and pick the largest they share, or use prime factorization and multiply the common primes.
How is the GCF used with fractions?
Dividing a fraction's numerator and denominator by their GCF reduces it to lowest terms in a single step.