# Greatest Common Divisor

Created By : Prasanna
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023

GCD Calculator is a handy tool that makes your calculations quick and simple. This online tool is the best for doubt clearance and concept learning. All you have to do is insert the given number in the designated field of the calculator and click on the “calculate” button. That's it, you will get the greatest common divisor of given numbers in a fraction of seconds with the explanation.

GCD Calculator: Tired of performing all those long , boring calculations which only makes your concepts more tangled up while increasing doubts. Not anymore with our GCD Calculator tool you can not only calculate with an impeccable speed but can do it while understanding the concepts alongside with our side by side explanation of the process. So, use this quick tool for solving your problems quickly.

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

## Why Calculate GCD?

GCD is basically used for calculating the common factor between fractions so that fractions can be expressed in simple form. Also, there are some applications where GCD is used, one of them is the public key encryption technique called the RSA algorithm. It is also used in higher forms of arithmetic called modular arithmetic.

### Difference between LCM and GCD

Least common multiple (LCM) is the smallest number divisible by a given set of numbers with no remainders. The greatest common divisor (GCD) is the highest number which divides the given set of numbers completely. We can find the GCD of a number by dividing the product of a given set of numbers by the LCM of a number.

### GCD Calculation with Steps

Here are the steps to calculate the GCD while using the LCM of numbers:

• Consider the given numbers.
• Calculate the LCM of these numbers using the long division method.
• Calculate the product of given numbers.
• Divide product of numbers by LCM of a number to get the GCD of numbers.

### How do you calculate GCD: Solved Example

Example:

Calculate the GCD of numbers 35 & 50.

Solution:

Here, the numbers are 35 & 50. Let us take their LCM using division method.

 35 50 2 35 25 5 7 5 5 7 1 7 1 1

Here, LCM (35, 50) = 2 x 5 x 5 x 7 = 350

Now, product of given numbers = 35 x 50 = 1750

Now the GCD (35, 50) = product of given numbers / LCM of same numbers

= 1750 / 350 = 5

GCD (35, 50) = 5

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### FAQs on Online GCD Calculator With Steps

• Are GCD and GCF the same?

Yes, Greatest Common Divisor (GCD) can be referred to as Greatest Common Factor(GCF).

• How do you make a GCD of two numbers greater than 1?

Most commonly to make GCD greater than 1, of all the elements in an array we perform several operations on the array like choosing an index and then replacing the numbers. With the help of some operations performed the resulting array comes out to be the best.

• What is the GCD of 2 and 4?

The common factors among 2 and 4 are only 1 and 2 thus, the Greatest Common Factor of 2 and 4 is 2.

• What is the GCD of two same numbers?

The Greatest Common Divisor of two same numbers would be the number itself.