Greatest Common Factor aka Greatest Common Divisor calculator is an online maths tool that finds the GCF of two or several numbers by all three GCF methods.

Through GCF (GCD) calculator, you can select the method of your choice. The GCF calculation through the selected method will be shown with a detailed explanation.

You can simply click on the other method to see its process, that is, you will not have to enter the values all over from the start.

## What is GCF?

Short form for Greatest Common Factor, GCF is the one factor that has the highest value among the common factors.

Other names of GCF include HCF and GCD.

## How to find GCF?

It is a little tricky to find GCF, that is why the GCF finder above is recommended. But for your information and concept, we will see how to find GCF in detail.

The famous methods used for calculating GCF are:

- Prime factorization
- Division method
- List of factors

You can see the example of prime factorization in the HCF and LCM calculator. In this post, we will learn the remaining two methods through examples.

**1. Division method:**

**Example:**

Find the GCF of **14** and **20** through the division method.

**Solution:**

**Step 1:** Use the higher value as a dividend and the lower value as the divisor.

Larger value = **20**

Lower value = **14**

**Step 2: **Divide by the nearest multiple.

The nearest value to 20 in 14’s times table is 14 itself.

**Step 3:** Continue until no more can be solved. The last divisor is **GCF (HCF)**.

**2. List of Factors:**

**Example:**

What is the greatest common factor of **12**, **16**, **29**? Use the **list of factors** method.

**Solution:**

**Step 1:** Write all the factors of **12**, **16**, and **29**.

Factors of **12** = **1**, **2**, **3**, **4**, **6**, **12**.

Factors of **16** = **1**, **2**, **4**, **8**, **16**.

Factors of **29** = **1**, **29**.

**Step 2: **Look for the common factors.

There is only one common factor of these three numbers i.e **1**.

**Step 3:** Identify the greatest common factor.

Since there is no other factor, **1** will be the GCF of **12**, **16**, and **29**.