Greatest Common Factor (GCF)

The greatest common factor

(GCF) of two or more numbers is the largest number that divides evenly into each of those numbers.

To find the GCF of two numbers, you can list the factors of each number and then find the largest factor that they have in common. For example, to find the GCF of 12 and 18, you would list the factors of 12 (1, 2, 3, 4, 6, 12) and the factors of 18 (1, 2, 3, 6, 9, 18), and then find the largest factor that they have in common, which is 6. So the GCF of 12 and 18 is 6.

To find the GCF of more than two numbers, you can use the same process, listing the factors of each number and then finding the largest factor that they all have in common.

There are also mathematical methods to find GCF of two or more numbers, such as Euclidean algorithm or prime factorization. Euclidean algorithm is a method of finding GCF by repeatedly subtracting the smaller number from the larger one until a zero or a common factor is obtained. Prime factorization is a method of finding GCF by breaking the numbers down into their prime factors and then multiplying the common prime factors.

GCF is also known as the greatest common divisor(GCD) and it is used in many areas of mathematics such as number theory, algebra and geometry.