GCF Calculator

Find the greatest common factor of two or more whole numbers, also called the GCD or HCF, with the working shown step by step.

Enter two or more whole numbers, separated by commas or spaces.
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GCF
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Prime factorization method
    Euclidean algorithm

      What is the greatest common factor?

      A factor is a number that divides another number with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12, and the factors of 18 are 1, 2, 3, 6, 9 and 18. The factors they share are 1, 2, 3 and 6, and the largest of these, 6, is the greatest common factor.

      How to use the GCF calculator

      1. Type two or more whole numbers, separated by commas or spaces.
      2. The GCF appears instantly, along with the prime factorization of each number.
      3. For exactly two numbers, the Euclidean algorithm steps are shown as well.

      Method 1: Prime factorization

      Break each number into primes, then multiply the primes that appear in every number, using the lowest power.

      For 48, 180 and 300:

      • 48 = 2⁴ × 3
      • 180 = 2² × 3² × 5
      • 300 = 2² × 3 × 5²

      Only 2 and 3 appear in all three. The lowest powers are 2² and 3, so the GCF is 4 × 3 = 12. The 5 is left out because 48 has no factor of 5.

      Method 2: The Euclidean algorithm

      Divide the larger number by the smaller, then keep dividing the previous divisor by the remainder until the remainder is 0. The last non-zero remainder is the GCF. For 48 and 180:

      180 = 3 × 48 + 36
      48 = 1 × 36 + 12
      36 = 3 × 12 + 0

      The last non-zero remainder is 12, so GCF(48, 180) = 12.

      Where the GCF is used

      • Simplifying fractions: divide the top and bottom by their GCF. 84/126 becomes 2/3 because the GCF is 42.
      • Making equal groups: with 48 pencils and 180 erasers, the largest number of identical kits you can make with nothing left over is 12, each with 4 pencils and 15 erasers.
      • Tiling and cutting: the largest square tile that fits a 48 × 180 inch area exactly is 12 inches on each side.
      • Factoring algebra: pulling out the GCF is the first step in factoring expressions like 12x + 18 = 6(2x + 3).

      Need the smallest shared multiple instead? Use the LCM calculator.

      Last reviewed October 2026.

      Frequently asked questions

      Is the GCF the same as the GCD or HCF?

      Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) all mean the same thing: the largest number that divides each of the numbers evenly.

      What does it mean if the GCF is 1?

      It means the numbers share no common factor other than 1. Such numbers are called relatively prime or coprime. For example, 8 and 15 are coprime even though neither is a prime number.

      How do I use the GCF to simplify a fraction?

      Divide the top and bottom of the fraction by their GCF. For 18/24, the GCF is 6, so 18/24 = 3/4. After dividing by the GCF, the fraction is in its simplest form.

      What is the GCF of a number and 0?

      Every number divides 0, so the GCF of a number and 0 is the number itself. The calculator asks you to remove zeros because they do not change the answer.

      Can I find the GCF of more than two numbers?

      Yes. Enter as many whole numbers as you like. The GCF of a list is the GCF of the first two numbers, then of that result and the next number, and so on.

      Which method is fastest for large numbers?

      The Euclidean algorithm. It only needs repeated division, so it stays fast even for very large numbers, while factoring large numbers into primes can take much longer.