What is GCF and how students can calculate it?

How student calculate Greatest common Factor

After reading this article, you will understand the term GCF and how you can find it. Because we are providing all the details you need here to understand this concept of mathematics. 

What is GCF?

In mathematics, the greatest common factor is abbreviated as GCF and it is the number that can be equally divided into two numbers. 

For example, the greatest common factor HCF of 28 and 35 is 7.

The main common divider can also be considered the greatest common factor. 

Before finding the greatest common factor, you must have to separate all numbers into factors (smaller numbers that multiply together to get the original number). 

You must also compare all the numbers to see if the numbers share anything— if you do, then pick the largest of them. 

The largest common factor for numbers that do not share a different divider is 1.

The highest common factor HCF of any two or more than two numbers are the greatest whole number that can be divided by all the numbers. 

The other terms that are used for H.C.F. are 

  • Greatest common factor (GCF)
  • The greatest common denominator (GCD)
  • Highest common factor (HCF)
  • Greatest common divisor (GCD)

When you consider any number factor, we refer to any number which divides the number without any remainder. 

For instance, the factors for 24 are: 1, 3, 4, 6, 8, 12, and 24. These all factors are also called as multiples of number 24. 

What are the factors?

Without any of the remaining numbers, number 4 cannot split number 10. If we divide the number 10 by 4, it is apparent that the result is 2.5 which does not come under the integer figure. 

Thus, the number 4 cannot be described as a ten-factor. The factors are either less than or equal to the initial number.

Now that you’ve learned about multiples and factors, we will move forward to further explanation of methods to find out the GCF.

The most common factors are the simple and easy way of finding the numbers. 

Two key strategies are typically considered to be simple for anyone to calculate the number of HCFs. They are the Form and Division of Prime Factorization.

  • Method 1: we write down all the numbers and the common factors are defined from these. The GCF of these numbers is the most common element. This form is the one we discussed above.
  • Method 2: Each number is separated into its factor elements. We then label, including repeated, the common primary factors. Finally, the common primary factors are multiplied.

How do you find the greatest common factor?

Whenever you asked to find out the GCFs of any two or more than two numbers, we first list each number’s prime factors. 

The numbers result in the GCF due to several common factors. The largest common factor is 1 because there are no common primary factors.

It should be easy to find the GCF for a certain number. However, it is important to take several steps to achieve the right GCF. 

You have to locate both factors in both numbers, and then identify similar factors to identify the largest common factor of two given numbers.

Factorization method 

It is the most common and easy method for calculating the highest common factor. This method of factorization includes compiling the number of two or more variables or divisors. 

It is necessary to note the largest number or the highest when listing the divisors of a given number, which separates the numbers without leaving a remainder in general.


Q.1) Using the factorizing process, calculate the HCF of 18 and 32.


Factors of number 18 are considered to be 1, 2, 3, 4, 6, 9, and 18. 

(1 x 16, 2 x 9, 3 x 6, and 4 x 4)

We know that factors of 32 are 2, 4, 8, 16 and 32. (1 x 32, 2 x 16, 4 x 8)

Therefore, the GCF of the above example is apparently 3. 

Prime factorization method 

It is another easy and simple technique, involving two or more numbers called primary variables. 

We can also calculate the significant variables identical to the listed numbers. 

The result is primarily the most common primary variable, the most common element, or the highest common divider.

Division method 

Another interesting suggestion is the division approach for computing the HCF. In cases where it functions well is when two specified numbers need to be calculated.

You have to identify the larger and the smaller numbers of those two numbers. 

Then the larger number is split to smaller and the divider is then divided by a memorandum. 

That is the general approach to applying the process of division before the remaining zero is reached.

You must also be careful not to ignore several additional means to discover the largest or highest common number factor in different methods of calculating HCF.

GCF calculator

Basically, the GCF Calculator is an online tool that anybody can use to calculate HCF problems more easily. 

This calculator provides its services for everyone for completely free. 

If you are a student and searching for a GCF tool for solving your mathematical problem, it is definitely one of the most powerful and useful option to go with. 

It would naturally spare you from complicated lengthy and boring mathematical operations. 

The key advantage of the calculator is that the largest common element in the list of numbers from two to infinity is measured in a fraction of a second. 

The shortest and easiest way to measure GCF is utilizing an online resource among the methods we mentioned earlier.

About author


Morris is a Technology enthusiast and a writer by night. He has been a part of TheTechly for quite some time and he contributes knowledgeable news articles from the Technology niche.
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