# Greatest Common Factor

Created By : Bhagya
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023

It is too time-consuming, challenging and tiresome when we solve the questions to find their Greatest Common Factor. But don't worry we have got the tool just for you our Greatest Common Factor Calculator. Get your calculations done in a fraction of a second with precision. Provide the numbers in the given place and click the “calculate” button to proceed with the calculations.

Greatest Common Factor of:

Here are some samples of Greatest Common Factor of Numbers calculations.

Related Calculators:

Greatest Common Factor Calculator: Questions getting too big, excruciating and uninteresting, concepts getting too difficult and entangling for you to understand then GCF (Greatest Common Factor) is something that can help you with all this. We present to you are very easy-to-use tool Greatest Common Factor Calculator that not only gives you answers at a quick pace in no time but also provides procedures for you to understand the concept briefly and easily.

### List of Greatest Common Factor Calculators

Apart from the procedures on Greatest Common Factor Concept, you will also find some useful & handy Greatest Common Factor (GCF) Calculators via direct links. Access them online whenever you need within a few taps you'll just attain the accurate results for your easy to complex GCF problems. The list of free online GCF Tools are as follow:

Okay, Let's get into this Greatest Common Factor Tutorial and become a great solver in the GCF concept. Now, we'll start learning with the Basics of GCF like Greatest Common Factor definitions, Other names of GCF, and Finding GCF of Numbers with numerous methods.

## What is the Greatest Common Factor?

In mathematics, a factor is a number or algebraic expression that divides another expression and leaves no remainder behind. In different words, if multiplying a set of whole numbers delivers us a product, then the set of numbers we are multiplying are the factors of the product because they are its exact divisor.

Additionally, Factors common in two or more numbers are called common factors.

Therefore, the Greatest common factor is nothing but the largest of all the common factors in a set of numbers.

The "Greatest Common Factor" is represented as "GCF", and is also called

the Greatest Common Divisor (GCD), or

the Highest Common Factor (HCF).

### GCF of Zero

As we clearly know that the division by zero is indefinite, so zero can not be a factor of any natural number.

Therefore, the Greatest common factor(GCF) or Highest common factor(HCF) of zero is undefined.

### Calculating Greatest Common Factor With Steps

Method 1: Listing all the factors to find the GCF

This method for finding the Greatest Common Factor is the easiest method when you have to deal with smaller numbers. To reveal the GCF of a set of numbers,

1. Firstly, Note down all the factors of each number.
2. Find the common factors.
3. Find the greatest factor existing on the common factor list.
4. Finally, the greatest common factor is found.

Method 2: Using prime factorization to find the GCF

This method works best for large numbers as making a list of all the factors can be time-consuming in larger numbers.

To find the GCF of a set of numbers using prime factorization:

1. List the prime factors of all the numbers.
2. Circle every prime factor that’s present in the numbers. In other words, circle every common factor.
3. Multiply all the numbers that are circled.
4. Finally, the Greatest common factor.

### Solved Example Find the Greatest Common Factor

Example:

Find the GCF of 9, 20, and 25. by listing the factors.

Solution:

The Factors of 9 are 1, 3, and 9

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

The Factors of 25 are 1, 5 and 25

Here, in this case, the only factor that comes out in all three number lists is 1, so 1 is the GCF of 9, 20, and 25.

Example:

Evaluate the Greatest Common Factor of 168, 252, and 288 by the prime factorization method.

Solution:

The given numbers are 168, 252, and 288.

Firstly, do the prime factorization of the given numbers.

168 = 23 × 3 × 7

252 = 22 × 32 × 7

288 = 25 × 32

The GCF of these sets of numbers will be the product of the smallest power of each common prime factor of the three numbers. Therefore, the Greatest Common Factor or GCF of 168, 252, and 288 = 22 × 3 = 12.

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### FAQs on Greatest Common Factor Calculator with Steps

• How do you calculate the greatest common factor?

The calculation for the greatest common factor begins with listing out the prime factors of the selected numbers and then multiplying them to get the GCF.

• How do you factor polynomials without GCF?

You try factoring by grouping when you want to factor the polynomials without GCF.

• What is the greatest common factor of 12?

First list all the factors of 12,

1,2,3,4,6,12

Now listing the factors of 16,

1,2,4,8,16

Hence the greatest common factor is 4.

• Find the greatest common factor of 21 and 28?

7 is the greatest common factor of 21 and 28.