How students can find the greatest common factor easily

Starting from primary education and till University studies, the greatest common factor is not a difficult task to find but when we talk about multiple numbers, it might create complexity.

For this, online calculators are useful and flexible for students to make their work done quickly. However, selecting an appropriate HCF finder is also a difficult task.

This is because hundreds of calculators that are available online but all have different features of displaying the highest common factor.

Not only this, but you also need to get the right calculator for you because some online calculators create mistakes when making the result.

In this article, we will discuss the ways of finding the highest common factor as well as the online calculators that can help you.

What is Greatest common factor and how do we find it?

The greatest common factor is the highest number between the factors of two or more values. For example, the GCF of 20, 40, and 180 is 20.

Factors of 20 = 1, 2, 4, 5, 10, 20

Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40

Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45,60, 90, 180

Now, we get the common factors as

Common factors of 20, 40, 180 = 1, 2, 4, 5, 10, 20

And the highest number is considered to be the greatest common factor, which is 20.

There are different methods of finding the highest common factors including manual calculation and online calculators.

However, the HCF is also findable through different methods and some of these are written below:

  • List of factors
  • Prime Factorization
  • Division Step
  • Euclidean algorithm
  • Binary Algorithm
  • Upside Down Vision

These types include different steps for finding the highest common factor.

Below, we have written the method involved in all of these methods.

GCF by List of factors

This is one of the most used especially for primary students because it is very easy as well as it has fewer chances of mistakes. In this step, you have to find the factors of all the numbers while the values should be more than 2.

When you list down all the factors, you need to find the largest number in these factors, and this way, the GCF would be found.

Prime factorization

In the prime factorization method, you have to make the prime factors of all the numbers whether it is two or more.

However, once you find it, find the common factors whether they are repeating and multiple all of these factors between the number.

Through multiplying, you can easily know the highest common factor of these numbers. If the common factor between the values is only one you won’t need to multiply it.

Division Method

This method is another popular way as well as it is also known as the factors tree method. In this method, you have to divide the number with the smallest number (which is usually 2).

Later, divide the divider by the remainder and repeat all of these steps until the remainder becomes 0. Before the remainder is zero, the last divisor is the highest common factor.

Euclidean algorithm

This is the Standard approach by most of the students around education. In this step, you have to find the whole number for integer a and b, in the way that the = bq + r, 0< r < b.

When the r = 0, then b is the GCF but when the r is not 0 then apply this algorithm to b and r.

Top calculators for finding the greatest common factor

Different calculators can be used for finding the greatest common factor automatically. But the task is that you should consider the best one to avoid any mistake.

Here, we have tested some of the best online calculators, and here are the results:


GCF finder by Meracalculator is one of the famous brands for various calculators including Physics, Mathematics, Chemistry, Finance, and other conversion calculators.

However, one of the best calculators is Highest common factor which provides an accurate result for different values.

How students can find the greatest common factor easily

This calculator is famous because it provides the results in multiple ways. It includes six methods for finding the HCF including the List of factors, Prime Factorization, Division Step, Euclidean algorithm, Binary Algorithm, and Upside-Down Vision.

You don’t need to register instead you can easily find the answer instantly. And upon clicking the method, it not only tells the result instead it shows the method of finding the method.

When you have to find the method according to your type then click on the tab in the results to get the steps according to your desire.

This tool is completely free while you don’t need to register, subscribe, or play a game to access this calculator.

Emathhelp  is another website that is best to find the highest common factor for multiple values. However, the best part is that it is also entirely free to use.

Greatest common factor in essay

This tool also shows all the steps taken for finding the result and this way, you can easily know the way to learn. Although this tool only gives the option for finding the GCF with two methods including simple factorization and prime factorization.

This math calculator website is popular among the students because of the simple user interface. is also offering the HCF calculator for free with simple usage. You just need to enter the values and instantly, it will give the results to you.


The decimal info doesn’t require any registration process or subscription to create the factors for you.


Sometimes, in education, you might require to find the highest common factors for the numbers that are more than two. In this situation, the manual calculation might be difficult because it would take a lot of effort and time to calculate, and still, you would have a chance of low accuracy.

For this, you should consider using online calculators that are fast and accurate as compared to the manual calculation.

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