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GCF Calculator greatest common factor

Enter your numbers to get the GCF (also called the GCD or HCF), with the shared primes at their lowest powers and a cross-check for two numbers.

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Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

Inside every GCF answer

  • Prime factorizations

    48 = 2⁴ × 3, 180 = 2² × 3² × 5 and 300 = 2² × 3 × 5² are listed, so you can see which primes they share.

  • Lowest common powers

    Only primes found in every number count, each at its smallest exponent: 2² × 3 = 12.

  • Euclid's algorithm for pairs

    With exactly two numbers, the division-with-remainder method is written out line by line as an independent check on the factorization.

  • Coprime detection

    If the numbers share no prime, the GCF is 1 and the result says they are coprime (relatively prime), as with 8 and 15.

Finding the GCF here

  1. Enter the numbers

    Type at least two positive integers with commas between them, such as 48, 180, 300. Up to 500 numbers are accepted.

  2. Press Calculate

    The GCF arrives as an exact whole number, so nothing is rounded and no ≈ mark appears, followed by the factorizations and a step outline. Your browser does the computing; there is no fee and no sign-up.

  3. Copy it or ask for more

    Copy the result, or have the AI Math Solver explain the method in prose via “Explain step by step”. AI explanations can include mistakes, and the step outline remains the reference.

How to find the GCF by hand: primes and Euclid

With prime factorization, break each number into primes, keep only the primes that appear in all of them, and use the smallest power of each. 48 = 2⁴ × 3, 180 = 2² × 3² × 5 and 300 = 2² × 3 × 5². The prime 5 is missing from 48, so it is dropped; 2 appears at least squared and 3 at least once. The GCF is 2² × 3 = 12.

Euclid's algorithm skips factoring. Divide the larger number by the smaller and keep the remainder, then repeat with the divisor and the remainder until the remainder is 0. For 180 and 48: 180 = 3 × 48 + 36, then 48 = 1 × 36 + 12, then 36 = 3 × 12 + 0. The last non-zero remainder, 12, is the GCF.

The GCF is the key to simplifying fractions. Because the GCF of 48 and 180 is 12, the fraction 48/180 reduces to 4/15 in a single step. When the GCF is 1, a fraction is already in lowest terms.

A quick check: dividing each number by the GCF should leave results with no common factor. 48, 180 and 300 divided by 12 give 4, 15 and 25, and nothing above 1 divides all three.

Frequently asked questions

Yes. Greatest common factor, greatest common divisor and highest common factor are three names for the same number; the wording depends on the country and the textbook.

Euclid's method works on one pair at a time. For three or more numbers the prime factorizations carry the whole answer, since they handle any count in one pass.

Two numbers are coprime when their only common factor is 1. 8 = 2³ and 15 = 3 × 5 share no prime, so their GCF is 1 even though neither number is itself prime.

Yes, when that number divides all the others. The GCF of 6, 18 and 24 is 6.

Only the optional AI explanation does. The Pro plans* include it (*fair use: up to 300 runs every day across the writing, study and code tools), it costs 2 credits for accounts without a plan, and a signed-out visitor sees a free preview of its start. Finding the GCF itself is free and private.

Checking your own answers is exactly what it is for. Do the factoring yourself first, and follow your teacher's rules on calculators and AI tools for anything that is graded.

Related number tools

Need the greatest common factor?

Enter your numbers and see the shared primes, with Euclid's algorithm as a check for pairs.

Find GCF
  • Two or more numbers
  • Coprime pairs flagged
  • Euclid cross-check