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Greatest Common Factor Calculator

Enter two or more numbers separated by commas to find their greatest common factor (GCF), least common multiple (LCM) and prime factorization.

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Greatest Common Factor (GCF) Calculator

GCF & Divisor Result

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Definition: Largest shared divisor
Method: Euclidean algorithm or prime factors
Inputs: Two or more numbers
Use case: Simplifying fractions, grouping, layout

What is the greatest common factor?

The greatest common factor of a set of numbers is the largest whole number that divides every one of them without a remainder. For 24, 36 and 60, the GCF is 12 because 12 divides all three and nothing larger does.

There are two common methods: the Euclidean algorithm (repeated division) and prime factorization (multiply the shared prime factors at their lowest powers). The calculator uses the fastest reliable approach and also shows the LCM, since the two are related by LCM(a,b) × GCF(a,b) = a × b.

Why the GCF matters

The GCF is the key to simplifying fractions: 18/24 reduces to 3/4 because both divide by 6, their GCF. It also helps split groups evenly, arrange tiles or photos into grids, and combine measurements in recipes.

Finding the GCF of three or more numbers works the same way: compute the GCF pairwise, or factor all numbers and take the common prime factors. The calculator handles any list you type.

How to use this calculator

  1. Type the numbers separated by commas, for example 24, 36, 60.
  2. Press Calculate GCF.
  3. Read the GCF and LCM of the whole list.
  4. Check the prime factorization of each number to confirm.

Pro tips

  • Use the GCF to simplify fractions instantly: divide top and bottom by it.
  • The GCF of two co-prime numbers is always 1.
  • The GCF of a set is never larger than the smallest number in the set.

Advantages & considerations

✅ Advantages

  • Works with two or more numbers
  • Shows LCM and prime factorizations
  • Instant answers for fraction simplification

⚠️ Considerations

  • Only accepts positive integers
  • Numbers must fit in standard integer precision

Frequently asked questions

What is the GCF of 24 and 36?▶
12. It is the largest number that divides both: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36, so the largest shared one is 12.
How is GCF calculated?▶
By the Euclidean algorithm or by multiplying the common prime factors at their lowest powers. Both give the same result.
What is GCF used for?▶
Simplifying fractions, distributing items into equal groups, and arranging things into even grids or layouts.
What is the GCF of two prime numbers?▶
1, because primes have no common factor other than 1. Such numbers are called co-prime.
What is the difference between GCF and LCM?▶
The GCF is the largest shared divisor, while the LCM is the smallest shared multiple. They are related by LCM × GCF = product of the two numbers.