Greatest Common Divisor

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

If you are looking for help on the Concept Greatest Common Divisor then you have come the right way. We have listed all about the GCD like Definition, GCD finder methods along with solved examples. Decide your favorite method among the following and check out yourself. Master the concept in a better way taking the help of the information provided here.

Ex: Greatest Common Divisor of 24, 48, 64 (or) Greatest Common Divisor of 16, 56, 12 (or) Greatest Common Divisor of 8, 72, 48

Greatest Common Divisor of:

Here are some samples of Greatest Common Divisor Numbers calculations.

Related Calculators:

Get to know complete details like GCD Definition, Other Names, How to solve GCD easily. You will also find related stuff such as GCF of two numbers, GCF of two or more numbers, GCF of Decimals, GCF of Fractions, etc.

List of Greatest Common Divisor Calculators

Along with the regular and manual procedures for finding the Greatest Common Divisor we have listed the simple and easy-to-use online tools. You can find the GCD, GCF, or HCF instantly from the below available links. Simply tap on the quick links depending on your need to attain faster and accurate results. They are as follows

  • GCF Calculator
  • Greatest Common Factor
  • 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
  • HCF Questions

Let's not wait anymore and learn the concept of GCD completely by proceeding further. Be aware of the Basics of GCD such as Definitions, Related Terms, and Different Methods of finding the GCD.

Basics about Greatest Common Divisor

Let's get started with some of the fundamentals regarding GCD like Factors, Common Factors, Prime Factors. Understand the concepts much better by referring to further modules.

What is a Factor?

The factor is one of the main concepts in Mathematics and it is needed to understand various concepts. As per general definition, a Factor is a number that divides into another number exactly i.e. without leaving a remainder. However, a number can have many factors.

Example: Factors of 10 include 1, 2, 5, 10 the numbers that divide exactly without leaving a remainder.

What is a Common Factor?

In general, Common Factor is a number that can be divided into two different numbers leaving a remainder zero. Finding Common Factors is possible if you have at least two numbers. In fact, you may have more than one common factor for numbers.

After finding the Factors of given numbers the factors which are common or same for both the numbers are called Common Factors

Example: What are the Common Factors of 25, 20?

Factors of 25 are 1, 5, 25

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

Finding the Common Factors from the factors list obtained for both the numbers

Common Factors for 25, 20 are 1, 5

What are Prime Factors?

Prime Factors play a key role in finding the Greatest Common Divisor. Get to know about the definition of Prime Numbers along with the procedure to find Prime Factors easily. A Factor that is a prime number and when multiplied results in the original number are called Prime Factors. For example, Prime Factors of 10 are 2 and 5.

Now that you are aware of all the fundamentals related to Greatest Common Divisor or Greatest Common Factor go ahead and learn even more like GCD Definition, Methods to find it.

What is meant by Greatest Common Divisor(GCD)?

Greatest Common Divisor or Highest Common Factor is the highest number that divides the given numbers exactly. For instance, GCD for a set of numbers 18, 30, 42 GCD is 6 the largest number that divides all three numbers leaving remainder zero.

Why GCD is Important?

Greatest Common Divisor is important in various math applications like simplifying polynomials where you need to figure out the common factors. You can simplify complex problems easily by employing the Concept of GCD or GCF.

See help from to know all about the GCF, LCD, LCM, HCF Concepts, and understand them easily.

Other names of Greatest Common Divisor

Greatest Common Divisor(GCD) is also referred to as Greatest Common Factor(GCF), Highest Common Factor(HCF), Greatest Common Denominator(GCD).

How to Find the Greatest Common Divisor?

There are several methods that help you find the GCF. Some of them can be a child's play while the rest may be complex. Check out each of the techniques and choose the one that suits your understanding and decide on your own.

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

Get to know the detailed procedure by tapping on the links mentioned above. You will be redirected to each of the procedures for finding the Greatest Common Factor. Make use of the solved examples provided for all the techniques and understand the concept better.