GCF Calculator

What Is the Greatest Common Factor (GCF)?

The greatest common factor — also called the greatest common divisor (GCD) or highest common factor — of two or more whole numbers is the largest number that divides all of them without a remainder. For example, GCF(32, 256) = 32. Type your numbers, separated by commas, into this GCF calculator to get the answer for two numbers or a longer list.

Method 1: Prime Factorization

Break each number into its prime factors, pick out the primes they have in common, and multiply those together. 16 = 2 × 2 × 2 × 2 and 24 = 2 × 2 × 2 × 3, so they share 2 × 2 × 2 = 8, and GCF(16, 24) = 8. This is easy for small numbers but slow when the numbers are large and hard to factor.

Worked Example

The GCF of 24 and 36 is 12 — the largest number that divides evenly into both.

Method 2: The Euclidean Algorithm

A far more efficient approach goes back to ancient Greece. Divide the larger number by the smaller and keep only the remainder; then repeat with the smaller number and that remainder, until the remainder is zero. The last non-zero remainder is the GCF. For 48 and 18: 48 ÷ 18 leaves 12; 18 ÷ 12 leaves 6; 12 ÷ 6 leaves 0, so GCF = 6. Even numbers with six digits take only a handful of steps. For three or more numbers, find the GCF of the first two, then the GCF of that result and the next number.

Where You Will Use It

• Simplifying fractions: divide the numerator and denominator by their GCF to reduce to lowest terms (see the Fraction Calculator).
• Simplifying ratios: 20 : 30 reduces to 2 : 3 by dividing both by 10.
• Splitting things evenly: the GCF tells you the largest group size that divides several quantities with nothing left over — for example, how many identical gift bags you can make from 24 pencils and 36 erasers (12).
• Number theory and cryptography, where gcd calculations underpin many algorithms.

GCF and LCM

For two numbers, GCF × LCM = a × b. If you know one, you can find the other. See the LCM Calculator for the other half.