Finding the Greatest Common Factor of 12 and 20 is a simple process that only requires basic knowledge of factors and divisibility. Before we dive into the actual process of finding the GCF, there are a few things we need to understand.

Firstly, what is a factor? A factor is a number that divides evenly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Next, what is divisibility? Divisibility is the ability for one number to be divided by another number without leaving a remainder. For example, 12 is divisible by 2, 3, 4, and 6 but not by 5 or 7.

Now that we understand these basic concepts, let’s move onto the process of finding the GCF of 12 and 20.

Step 1: Find the factors of both numbers.

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

Step 2: Identify the common factors.

The common factors of 12 and 20 are 1, 2, and 4.

Step 3: Determine the greatest common factor.

Out of the common factors, the greatest common factor is 4 as it is the largest factor both numbers share. Therefore, the GCF of 12 and 20 is 4.

To check if we have found the correct GCF, we can divide both numbers by 4.

12 ÷ 4 = 3

20 ÷ 4 = 5

Both 3 and 5 are prime numbers which means they cannot be divided further. This confirms that 4 is indeed the GCF of 12 and 20.

In conclusion, finding the GCF of 12 and 20 involves finding their factors, identifying the common factors, and then determining the greatest common factor. The process is simple and can be applied to any two numbers.