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What is GCF? Explain in detail



In Mathematics, a factor is numerical, which gets the desired numbers when multiplied by other numbers. Usually, the numbers can be factored into various combinations and operations. The factors can be easily figured out if you are accustomed to the multiplication tables. Here, we are going to discuss what is the greatest common factor and how to find GCF with a few examples.

What is the Greatest Common Factor?

The most substantial number, which is the factor of two or more numbers, is called the Greatest Common Factor or also known as GCF. It is the largest number that splits them, resulting in a Natural number. Once all the factors of the number are found, few factors are standard in both. The largest number that is found common in the factors is called the greatest common factor. The GCF is also known as the Highest Common Factor or also known as HCF.

In order to get an in-depth understanding of the topic, students can practice multiple grade 6 math worksheets. Worksheets can help students solve a variety of questions related to GCF. Cuemath is an online learning platform that helps students explore the concept of GCF in the most interesting way. Cuemath worksheets are super fun and exciting thus creates an amazing learning experience for students.

How to Find the Greatest Common Factor?

If we have to find the GCF of two numbers, we will first list all the prime factors of all numbers. The multiple common factors of both the numbers occur in GCF. If there are no common prime factors, then the greatest common factor is 1. Finding the GCF of a particular number set can be simple. However, some steps need to be followed to get the exact GCF. To find the greatest common factor of two given numbers, you need to group the factors of both the numbers and then distinguish the common factors.

Following are three methods for obtaining the greatest common factor of two numbers.

  • Listing Out the Common Factors
  • Prime Factorization
  • Division Method

GCF by Listing Out Common Factors

In this process, common factors of both the numbers can be arranged; it then becomes simple to check for the common factors. By identifying the common factors, we can choose the greatest one amongst all the factors. Let’s look at the example provided below:

Example: What is the GCF of 30 and 42?

  • Step 1 – List out all the factors of the given number. Factors of number 30 – 1, 2, 3, 5, 6, 10, 15, 30. Factors of number 42 – 1, 2, 3, 6, 7, 14, 21, 42
  • Step 2 – identify all the common factors.
  • Step 3 – 6 is the common factor and the greatest factor in the set.

GCF by Prime Factorization

Prime factorization is a way of denoting a number as a product of its prime factors, starting from the smallest prime factor of the given number. Let’s look at the example provided below:

Example 1: What is the GCF of numbers 60 and 90?

  • Step 1 – Copy the numbers in the prime factored form.
  • Step 2 – GCF is the product of the factors that are common to each of the provided numbers.

GCF by Division Method

The division method groups object in the same groups, whereas we follow a long division method for huge numbers. This breaks down a division problem into a series of more comfortable steps. The greatest common factor of a set of whole numbers is the greatest positive integer that divides uniformly into all numbers without giving any remainder.

Greatest Common Factor of Multiple Numbers

Now, if there are more than two numbers, students should list out common factors that become difficult. Thus, we can practice either of the methods: Prime Factorization or the Long Division.

Difference between GCF and LCM

The GCF of two or more numbers is the greatest factor among all the common factors of a particular set of numbers. In contrast, the LCM of two or more numbers is the smallest number between all common multiples of the provided numbers.


GCF is a vital and fundamental concept in mathematics. Students can solve and practice problems related to GCF with worksheets and workbooks available freely online.



I'm Nikos Alepidis, blogger at motivirus. I'm passioned for all things related to motivation & personal development. My goal is to help and inspire people to become better.

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