# GCF

GCF stands for Greatest Common Factor, which is the largest number that divides two or more numbers without leaving a remainder. It is also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

To find the GCF of two or more numbers, you need to find all the factors of each number and then identify the greatest factor that is common to all the numbers.

For example, let’s find the GCF of 12 and 18:

The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 12 and 18 are 1, 2, 3, and 6. Therefore, the GCF of 12 and 18 is 6.

You can also use the prime factorization method to find the GCF of two or more numbers. First, express each number as a product of prime factors, and then identify the common factors and multiply them together.

For example, let’s find the GCF of 24 and 36 using the prime factorization method:

The prime factorization of 24 is 2^3 x 3. The prime factorization of 36 is 2^2 x 3^2. The common factors are 2^2 and 3. Therefore, the GCF of 24 and 36 is 2^2 x 3, which is 12.

### To find the greatest common factor (GCF) of two or more numbers, you can use the following step-by-step process:

1. List the factors of each number.
2. Identify the common factors that are shared by all the numbers.
3. Find the greatest of these common factors.

Let’s go through an example to illustrate this process.

Example: Find the GCF of 24, 36, and 60.

1. List the factors of 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.
• The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
1. Identify the common factors:
• The common factors of 24, 36, and 60 are 1, 2, 3, 4, 6, and 12.
1. Find the greatest common factor:
• The greatest common factor of 24, 36, and 60 is 12.

Therefore, the GCF of 24, 36, and 60 is 12.