Greatest Common Factor Calculator

The greatest common factor of two or more non-zero integers is the largest positive integer that divides each of the numbers without leaving a remainder. There are two primary methods to find the GCF: listing factors and prime factorization. When using prime factorization, you break each number down into its prime components, identify the shared prime factors, and multiply the lowest powers of those shared primes together to yield the final GCF value.

Let us find the greatest common factor of 24 and 36. First, list the positive integer factors for each number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Next, identify the common factors shared by both lists, which are 1, 2, 3, 4, 6, and 12. The largest number in this shared set is 12. Therefore, the greatest common factor of 24 and 36 is 12.

When working with large numbers, prime factorization is significantly faster than listing every single factor manually. If one number divides evenly into another, the smaller number is automatically the GCF of that pair. Additionally, if your numbers share no common prime factors other than 1, they are considered co-prime, meaning their GCF is always 1.