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Greatest Common Factor (GCF) Calculator

Greatest common factor and least common multiple of 2–10 numbers, with the Euclidean algorithm shown step by step and the prime factorization of every number.

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Parsing numbers
Running the Euclidean algorithm
Factoring into primes
Done

Result

This page opens the calculator with the greatest common factor highlighted as the main result: paste 2 to 10 whole numbers and run it to get their GCF, with every division of the Euclidean algorithm written out. For 48 and 180 the steps read 180 = 3 × 48 + 36, 48 = 1 × 36 + 12, 36 = 3 × 12 + 0 — so the GCF is 12.

The same quantity goes by several names — greatest common divisor (GCD), highest common factor (HCF) — and for more than two numbers the calculator folds them pairwise: gcd(a, b, c) = gcd(gcd(a, b), c). The prime factorization of each input is shown alongside, so you can confirm that the GCF collects exactly the prime powers shared by every number.

The GCF is what you need to reduce a fraction to lowest terms, to split items into the largest equal groups, or to find the biggest tile that fits a floor evenly. The least common multiple is computed in the same run, and the whole working can be copied as text with one click.

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Accepted Formats & Rules

  • GCF and LCM of 2 to 10 whole numbers in one run.
  • Step-by-step Euclidean algorithm and the lcm(a, b) = a × b ÷ gcd(a, b) working shown.
  • Prime factorization of every number in exponent form (48 = 2⁴ × 3).

Key Benefits

✓ Shows every division of the Euclidean algorithm, so the GCF is not just an answer but a worked example.
✓ Exact big-integer arithmetic: the LCM of many large numbers is computed without overflow or rounding.
✓ Prime factorization of each input in exponent form makes the shared and missing factors obvious.

Use Cases

  • • Find the GCF of 48 and 180 with every Euclidean division written out, to reduce a fraction or check math homework.
  • • Compute the LCM of several numbers to find a common denominator or the moment repeating schedules line up again.
  • • See the prime factorization of each number in exponent form (48 = 2^4 × 3) to understand which factors are shared.