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Last updated date: 17th Apr 2024
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Introduction to GCF

Greatest Common Factor or GCF is the largest number and a factor of two or more numerical. These factors upon diving results in natural numbers, and they are essential to develop knowledge in multiplication and factors for attempting any equation in future. Students are aware of this basic concept; however, it is integral that they study in detail to attempt mathematical problems with ease.

GCF offers students with a clear idea of factors and multiples of each number. It also enables them to understand which number is divisible and which isn't.

What is a Common Factor?

Before deciphering the meaning of common factors, students must clearly understand what a factor is. A number that is divisible by any other numerical and does not leave remainders is a factor. Most numerical numbers have an even number as a factor, and square numbers have an odd number. To comprehend the concept of a common factor, you will need a proper example.

Factors of number 10 are 1, 2, 5 and 10 while 15 are 1, 3, 5 and 15. The common factor here is 1 and 5.

Therefore, common factors are a number divisible by two or more numerical and don't leave behind a remainder. Often numbers share more than one common factor. Students can also attempt to find common factors of more than one number with ease.

What is the Greatest Common Factor?

Greatest common factor of a number is the largest integer that can divide it without leaving a remainder. When you divide two numbers, you get certain common integers, and among these factors, the highest number is called GCF.

Here is an explanation to help you understand what is GCF:

Three numbers 18, 30, and 42.

Among these numbers, factors of 18 are 1, 2, 3, 6, and 18.

Factors of 30 are 1, 2, 3, 5, 6 and 30.

Finally, factors of 42 are 1, 2, 3, 6 and 7.

By deriving each of these numbers' factors, common factors include 1, 2, 3 and 6. Among these factors, GCF is 6.

Therefore, it is the highest possible multiple among all divisible factors of these three numbers.

How to Find GCF?

The process of finding the Greatest Common Factor is simple and requires students to be acquainted with its formula. Students will need to have proper knowledge of multiplication and division when attempting these equations.

Before you learn how to find the greatest common factor of two or more numbers, you will need to list all prime numbers of each every numerical. The common factor which is a multiple of both numbers will result in GCF. In case a student is unable to determine GCF, then they will need to keep prime factor 1 as their greatest common factor.

To find greatest common factor and how you derive it, you will first need to consider the same example.

For numbers 18 and 24, GCF is 6.

This is because the common factor for these two number 1 × 2 × 3 = 6

The process to find GCF for two or more numerical can be easy. However, the method of finding a solution involves several steps. That is why students also need to comprehend these steps and related equations.

What is the Difference Between Highest Common Factor and Greatest Common Factor?

Highest common factor or HCF is greatest common divisor or GCF of two or more positive integer. Among these factors, whichever is highest is taken as the common factor. Usually, the highest common factors are directly divisible and don't leave behind any remainders.

Here is an example of HCF:

Let's take two numbers, 8 and 12.

Factors of 8 are 1, 2, 4, and 8. Factors of 12 include 1, 2, 3, 4, and 12.

Here the HCF of two integers is 4. This is because 4 is the highest factor that is common and divisible to two numbers.

Another factor that students will study while going through this topic would be the lowest common factor. As the name suggests itself, it refers to the lowest common factors divisible by the whole number. LCM is the smallest and least positive integer.

For example, consider two numbers 4 and 6.

Multiples of 4 include 4, 8, 12, 16, 20, 24, etc. On the other hand, multiples of 6 comprise 6, 12, 18, 24, 30, etc.

Therefore, common multiples here are 12, 24, 36, 48, etc. least common multiple here would be 12.

So, what is the GCF? The greatest common factor or the GCF is the greatest integer that is divisible by the numbers and doesn't leave behind any integers.

To understand how to get GCF, let's take the previous example.

If the common factors of 4 are 1,2, and 4 while the common factors of 6 are 1, 2, 3, and 6, then the GCF is 1 x 2 = 2. This is how you find the GCF.

Which App to Turn to When Studying Mathematical Equations?

Here is a list of several reasons you should use this application to study the greatest common factor definition.

  1. Application comprises videos that use illustrations to explain various mathematical topics.

  2. Languages in these live classes are simple and easy to comprehend for students.

  3. There are various exercises that students need to solve. Based on their performance, students receive points.

  4. By attempting these classes, the learning process becomes a bit smoother and easier for students.

  5. Teachers in online classes use plenty of examples to help keep students engaged and intrigued.

Therefore, by studying for this chapter through Vedantu app, you can develop a clear understanding of the GCF definition.


1. How to Find GCF?

Ans. To find GCF of any of factor, you will need to study multiplications and comprehend, which factor belongs to which the whole number. Therefore, it is important that when finding GCF, try figuring out each whole number's multiples. Afterwards, you can evaluate and factor out greatest common factor.

Factors of 12 are 1, 2, 3, and 12. On the other hand, a factor of 24 is 1, 2, 3, 4, 6, 8, etc. Here common factors are 2 and 3. Therefore GCF is 6.

2. What is the Difference Between HCF and GCF?

Ans. HCF and LCM are two different concepts. HCF of a number is the highest common factor. It is a number which is the highest of all factors. GCF is multiple of two common factors.

Like if common factors of 12 and 24 are 2 and 3, then HCF is three whereas GCF is 6.

3. What Real-Life Scenario can GCF Assist in?

Ans. Proper knowledge on this aspect will enable you to score well in your examinations. Although a beginner's chapter, it is an integral part of the examination. Also, knowledge on the subject will enable students to understand multiplication and tables with ease.