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What is the GCF Formula? How to Find the Greatest Common Factor(GCF) with LCM?

In this article, you will learn what is the greatest common factor and how to calculate GCF.


What is GCF?

GCF is the short form of the greatest common factor. It refers to the greatest common multiple of two or more integers that divides them. It is necessary to understand the concept of a factor to understand GCF. A factor can be defined as the multiple of an integer that divides it successfully.

For example, the 2, 3, 4, 6, and 8 are multiples of 24. So these are called factors of 24. Now the greatest common factor of 24 is the largest factor that divides 24, that is, 8.

The GCF is a basic mathematical concept used with fractions to simplify them. These factors simplify the fraction by dividing the denominator and numerator to write it in a simple form. It has many applications in real life.

How to Find the Greatest Common Factor?

The greatest common factor or GCF can be found by calculating all of the factors of each number and then selecting the greater factor from them, that will be GCF. See the example below to understand how GCF is calculated.

GCF Examples

find gcf with examples

find gcf with examples


GCF by Prime Factorization


GCF can also be found by using prime factorization of given numbers. It is a way to find the prime factor of a number that divides it.

GCF by Prime Factorization

GCF by Prime Factorization




The greatest common factor of two or more integers is a largest number in the common factors that divides the integers without leaving any remainder. For example, the GCF of 42 and 18 is 6 that divides both of them. Whereas the LCM refers to the least common factor that is the smallest multiple of two or more numbers that divides them without leaving a remainder. For example from the above example, the LCM of 18 and 42 will be 2.s

Frequently Asked Questions (FAQ’s)

What is GCF in Maths?

The GCF in maths is a greatest common factor of the given number that divides it without leaving a remainder.

What does GCF Mean?

GCF is the abbreviation of greatest common factor which means that highest common factor of two or more numbers.

What is the GCF of 4 and 12?

The factors of 4 are 1 and 2, and the factors of 12 are 1,2,3,4 and 6. So the GCF of 4 and 12 is 2.

Alan Walker

Last updated: July 07, 2023

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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