Greatest Common Factor

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Want to master in solving Greatest Common Factor in any mathematical concept problems with ease? Then, you need to understand and practice more and more with all standard & unique methods of finding the Greatest common factor of given numbers. Students should learn right from the definition of GCF to determining the greatest number with various methods in a better way.

Ex: Greatest Common Factor of 12, 48, 64 (or) Greatest Common Factor of 16, 56, 22 (or) Greatest Common Factor of 8, 72, 48

Greatest Common Factor of:

Here are some samples of Greatest Common Factor of Numbers calculations.

Related Calculators:

So, referring to this article gonna be the perfect guide to learn and master the concept of Greatest Common Factor. This guide includes GCF definition, other names of GCF, How to Find it easily, Factor and common factor definitions, and all related stuff like GCF of two numbers, GCF of three or more numbers, etc.

List of Greatest Common Factor Calculators

Apart from the procedures on Greatest Common Factor Concept, you will also find some useful & handy Greatest Common Factor (GCF) Calculators via direct links. Access them online whenever you need within a few taps you'll just attain the accurate results for your easy to complex GCF problems. The list of free online GCF Tools are as follow:

  • GCF Calculator
  • GCF of two or more Numbers Calculator (n numbers – comma separated)
  • GCF of 3 Numbers Calculator
  • GCF of 4 Numbers Calculator
  • GCF of Fractions Calculator
  • GCF of Decimals Calculator

Okay, Let's get into this Greatest Common Factor Tutorial and become a great solver in the GCF concept. Now, we'll start learning with the Basics of GCF like Greatest Common Factor definitions, Other names of GCF, and Finding GCF of Numbers with numerous methods.

All Basics About Greatest Common Factor(GCF)

Okay let's just begin with some basics like what is a factor, common factors, prime factors, and then we'll move to the Greatest common factor to understand the concept clearly and deeply.

What is a Factor?

In mathematics, one of the main concepts is Factor and it will be useful in many concepts. The general definition of Factor is a number that divides into another number exactly and without leaving a remainder. A number can have many factors.

Example: What are the Factors of 12? Factors of 12 are 1, 2, 3, 4, 6, and 12.

What is a Common Factor?

A common factor is a number that can be divided into two different numbers, with zero remainders. Usually, numbers can give more than one common factor. At least we need two numbers or more than two to find the common factors.

If you find the factors of any two numbers then the factors which are the same from both numbers can be known as "Common Factors".

Example: Here, we are considering three numbers ie., 105, 15, and 30 to find the Common Factors. Firstly, we need to compute the factors of three numbers then we get,

Factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105

Factors of 15 are 1, 3, 5, and 15

Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30

Now, find the factors that are common to all three numbers. Here we get, 1, 3, 5 and 15

Therefore, the common factors of 105, 15, and 30 are 1, 3, 5, and 15.

What is Prime Factors?

In maths, Prime Factors also acts a major role in calculating the Greatest common factor. Learn the definition of prime factors and find the prime factors for given numbers easily. A factor which is a prime number and it multiplies to give the original number is called a prime factor. For instance, the prime factors of 15 are 3 and 5.

Now, you've learned all fundamentals about the greatest common factor concept. So, let's get into the definition and detailed explanation on how to find the GCF of the given numbers.

What is the Definition of the Greatest Common Factor?

In a simple way, the definition of GCF is nothings but the largest of the common factors of two or more numbers that divide exactly, with zero remainders.

In the earlier example, we find the common factors for 105, 15, and 30 are 1, 3, 5, and 15.

Now, the GCF of 105, 15, and 30 is 15 (because the largest common factor that evenly divisible by the given numbers without leaving the remainder).

Why GCF is Useful?

We all know that fractions are very hard to simplify but with the Greatest common factor concept, the computation of fractions gonna be simple and easy.

Other names of Greatest Common Factor

The acronym of GCF is the Greatest Common Factor and also called as the "Greatest Common Divisor (GCD)", or the Greatest Common Denominator (GCD), or the "Highest Common Factor (HCF)".

Different Ways to Find the Greatest Common Factor (GCF)

There are numerous methods & techniques that can be possible to find out GCF of numbers. You can determine the greatest common factors for two numbers, GCF of 3 numbers or GCF of 4 or more numbers with these below provided standard and most prominent methods. They are as such,

  • GCF using List of Factors (Factoring) method
  • GCF of two Numbers using Prime Factorization method
  • GCF of three Numbers by Division method
  • HCF using Euclid's Division Lemma Algorithm
  • GCF of Numbers using GCD Formula

Make use of these accessible links and check out the detailed procedure that every method involve in solving the Greatest common factor. Also, you can discover solved examples for each and every technique from our articles, unlike other GCF tools.

So, visit and get full-fledged knowledge about GCF as well as LCM, HCF, LCD, GCD, etc.