# GCF (Greatest Common Factor) Calculator

The greatest common factor or GCF calculator is a tool that finds the highest value factor that is common for two or more numbers.

## Greatest Common Factor

The greatest common divisor calculator provides all of the common factors and then separately highlights the GCF. Users can find the GCF for 12 or fewer positive numbers.

## How to use the GCF calculator?

Follow the below steps to use the greatest common factor calculator above;

- Enter the number of positive integers.
- After that, input the numbers.
- Click find.

Right after you enter the number of integers, the same number of boxes will appear. You can use the GCF/GCD finder unlimited times.

## What is GCF?

You can define it as:

“Greatest common factor is the largest positive integer which divides the number without a remainder.”

For instance, the numbers 12 and 18 have the factors 1, 2, 3, and 6. And six (6) is the highest common factor (HCF) aka GCF.

It also goes by the name greatest common divisor or highest common divisor.

## Methods to find the GCF

There are 5 famous methods to calculate GCF. These methods are:

- Prime factorization
- List of factors
- Division method
- Euclidean Algorithm
- Upside down division

## How to find the greatest common factors?

In this section, we will teach you three out of the five common methods to calculate HCF. You can learn about prime factorization by visiting our prime factorization calculator.

**List of factors:**

You simply write all of the possible factors in front of the value and then identify the greatest of them.

Let’s see an example.

**Example:**

Find the GCF of **18** and **27** by the list of factors method.

**Solution:**

**Step 1:** List all the factors of 18.

* Factors of 18:* 1, 2, 3, 6, 9, 18

**Step 2:** Now, list all possible factors of 27.

* Factors of 27:* 1, 3, 9, 27

**Step 3:** Identify the common factors.

* Common factors:* 1, 3, 9

**Step 4:** Look for the biggest factor.

__Greatest common factor:__**9**

Before moving on to the next method, care to check out our HCF and LCM calculator?

**Division method:**

Using the division method you take two numbers and identify which one is smaller and which one is greater. Then you divide the greater number by the smaller number until the remainder is zero.

The division process is a little different. You divide first simply. But in the second step, you have to change the divisor and the dividend.

The remainder of the first step becomes the divisor and the divisor of the first step becomes the dividend.

**Example:**

Find the HCF of **18** and **48** by the division method.

**Solution:**

**Step 1:** Identify the divisor and the dividend.

Divisor = 18 (since smaller)

Dividend = 48

**Step 2:** Start dividing.

**Step 3:** Now take 12 as divisor and 18 as a dividend. Keep dividing until the remainder is zero.

If there are three values then the divisor and dividend remain the same. But the middle value is divided by the HCF of the greatest and the smallest value. And its last remainder becomes the HCF of all three values.

**Upside down division**

Also known as the ladder method, the upside-down division is probably the easiest way to find the GCF of two numbers.

You start off by placing both values in the general ladder division symbol. Then you divide the values by prime numbers in ascending order. And you keep on dividing if and only both values are divisible.

**Example:**

By the ladder method, find the GCF of **35**,**56**, and **63**.

**Solution:**

**Step 1:** Place the numbers.

**Step 2:** See which prime number can divide all three of these.

**2** can divide.

**Step 3:** Now, see if the same number can divide or not. If not then try the next prime number.

**2** cannot completely divide 15 and 39. But 3, the next prime number, can.

**Step 4:** On to the next prime number.

Since **3** cannot divide we see which next prime number can divide all three numbers. No can. So we stop here.

**Step 5:** Multiply the common prime factors to find GCF.

GCF of **35,56**, and **63** = 2 x 3 = **6**

## Table of Greatest Common Factor

Find the GCF of | GCF |

GCF of 18 and 27 | 9 |

GCF of 24 and 36 is | 12 |

GCF of 8 and 12 is | 4 |

GCF of 16 and 24 is | 4 |

GCF of 8 and 15 is | 1 |

GCF of 16 and 24 is | 8 |

GCF of 3 and 8 is | 1 |

GCF of 30 and 54 is | 6 |

GCF of 92 and 23 | 23 |

GCF of 5 and 20 is | 5 |

HCF of 7, 15, and 21 is | 1 |

HCF of 1, 20, and 150 is | 1 |

GCF of 3,4 and 6 is | 1 |

HCF of 10 and 45 is | 5 |

HCF of 680,510 and 340 is | 4 |

HCF of 45 and 81 is | 9 |

HCF of 27 and 63 is | 9 |

HCF of 12 and 48 is | 12 |

GCF of 31 and 62 is | 32 |

### References:

- How to Find the Greatest Common Factor | Varsitytutors.com
- Smartick.com | What is Greatest Common Factor (GCF).