GCF Calculator

How to Calculate the Greatest Common Factor (GCF)

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides each of the numbers without a remainder.

Formula

There is no single formula for calculating the GCF, but we can use the Euclidean algorithm:

\[ GCF(a,b) = GCF(b, a \bmod b) \]

Where:

• a and b are the numbers we're finding the GCF for
• a mod b is the remainder when a is divided by b

Calculation Steps

1. Take two numbers a and b.
2. Divide a by b and get the remainder.
3. If the remainder is 0, b is the GCF.
4. Otherwise, set a to b, b to the remainder, and repeat from step 2.

Example

Let's find the GCF of 48 and 18:

1. 48 ÷ 18 = 2 remainder 12
2. 18 ÷ 12 = 1 remainder 6
3. 12 ÷ 6 = 2 remainder 0

The last non-zero remainder is 6, so the GCF of 48 and 18 is 6.

Visual Representation

This diagram illustrates how 6 is the largest number that can evenly divide both 48 and 18.