This GCF calculator lets you calculate the GCF (greatest common factors) of upto $\hspace{0.2em} 15 \hspace{0.2em}$ numbers at a time. The calculator will tell you not only the GCF but also how to calculate it using different methods, like prime factorization and ladder methods.

Here's a quick overview of what the GCF is and how to calculate it.

For those interested, we have a more comprehensive tutorial on the greatest common factor.

## What Is the GCF?

The greatest common factor (or GCF) of a group of numbers is the largest number that is a factor of each of the given numbers. In other words, the GCF is the greatest of their common factors.

For example, consider the numbers $\hspace{0.2em} 3 \hspace{0.2em}$ and $\hspace{0.2em} 5 \hspace{0.2em}$.

- Factors of $\hspace{0.2em} 24 \hspace{0.2em}$ — $\hspace{0.2em} {\color{Red} 1} , \hspace{0.25em} {\color{Teal} 2} , \hspace{0.25em} {\color{Orchid} 3} , \hspace{0.25em} 4, \hspace{0.25em} {\color{DarkOrange} 6} , \hspace{0.25em} 8, \hspace{0.25em} 12, \hspace{0.25em} 24 \hspace{0.2em}$
- Factors of $\hspace{0.2em} 30 \hspace{0.2em}$ — $\hspace{0.2em} {\color{Red} 1} , \hspace{0.25em} {\color{Teal} 2} , \hspace{0.25em} {\color{Orchid} 3} , \hspace{0.25em} 5, \hspace{0.25em} {\color{DarkOrange} 6} , \hspace{0.25em} 10, \hspace{0.25em} 15, \hspace{0.25em} 30 \hspace{0.2em}$

As you can see, $\hspace{0.2em} {\color{Red} 1} \hspace{0.2em}$, $\hspace{0.2em} {\color{Teal} 2} \hspace{0.2em}$, $\hspace{0.2em} {\color{Orchid} 3} \hspace{0.2em}$, and $\hspace{0.2em} {\color{DarkOrange} 6} \hspace{0.2em}$ are the common factors of $\hspace{0.2em} 24 \hspace{0.2em}$ and $\hspace{0.2em} 30 \hspace{0.2em}$. And since $\hspace{0.2em} {\color{DarkOrange} 6} \hspace{0.2em}$ is the greatest of the common factors, it is their greatest common factor (GCF).

## GCF Calculation

There are variuos different methods to calculate the GCF, one of the most popular being the prime factorization method. Let me explain with an example.

### Prime Factorization Method

Say, you want to calculate the GCF of $\hspace{0.2em} 24 \hspace{0.2em}$, $\hspace{0.2em} 60 \hspace{0.2em}$, and $\hspace{0.2em} 84 \hspace{0.2em}$. Here's how you would go about it.

Step 1. Do the prime factorization of each of the numbers.

$\begin{align*} 24 \hspace{0.2em} &= \hspace{0.2em} 2 \times 2 \times 2 \times 3 \\[1em] 60 \hspace{0.2em} &= \hspace{0.2em} 2 \times 2 \times 3 \times 5 \\[1em] 84 \hspace{0.2em} &= \hspace{0.2em} 2 \times 2 \times 3 \times 7 \end{align*}$

Step 2. Identify the factors common to the prime factorization of the numbers. Note the instance of smallest exponent (or minimum repititions) for each of those factors.

Here, the common factors are $\hspace{0.2em} 2 \hspace{0.2em}$ and $\hspace{0.2em} 3 \hspace{0.2em}$.

Also, the smallest exponent of $\hspace{0.2em} 2 \hspace{0.2em}$ is $\hspace{0.2em} {\color{Red} 2} \hspace{0.2em}$ ($\hspace{0.2em} 2 \hspace{0.2em}$ occurs $\hspace{0.2em} {\color{Red} 2} \hspace{0.2em}$ times in $\hspace{0.2em} 60 \hspace{0.2em}$). Similarly, the smallest exponent for $\hspace{0.2em} 3 \hspace{0.2em}$ is $\hspace{0.2em} {\color{Teal} 1} \hspace{0.2em}$.

Step 3. Multiply together the factors raised to their respective powers to get the GCF. So,

$\begin{align*} \text{GCF} \hspace{0.3em} &= \hspace{0.25em} 2^ {\color{Red} 2} \times 3^ {\color{Teal} 1} \\[1em] &= \hspace{0.25em} 12 \end{align*}$