The greatest common divisor calculator is a free online tool that helps you to compute the greatest common divisor of any two numbers easily and quickly. To use this calculator, Give upto 2 numbers as inputs in the input fields and then click on the calculate button that gives you the answers instantaneously.
The greatest common divisor calculator is a free online tool that helps you to compute the greatest common divisor of any two numbers easily and quickly. To use this calculator, Give upto 3 numbers as inputs in the input fields and then click on the calculate button that gives you the answers instantaneously.
Greatest Common Divisor Calculator: If you are struggling to compute the GCD of numbers then this page is the right choice for you. On this page, you will see a GCD calculator tool that provides you with answers for any three numbers easily and quickly along with some simple guide for students to solve GCD easily
GCD(Greatest Common Divisor) is nothing but the common factor of both positive integers of (a,b). GCD is also defined as the greatest positive number. The common least positive integer in GCD is 1.
GCD Methods
As we have three methods to find the GCD of two numbers, we are looking into them below clearly.
Prime Factorisation Method
LCM Method
Euclid's Algorithm Method
Finding Common Divisors Method
Prime Factorisation Method
In this method, each method is written as the product of prime numbers and then we will find the smallest prime factors from all those numbers. And this method is applicable only for positive natural numbers.
LCM Method
In this LCM method, the GCD of any two positive integers a,b, is calculated by using the formula, i.e., GCD (a,b) = [a x b] /[LCM(a,b)]
Euclid's Algorithm Method
In this method, the GCD of two positive integers can be calculated by the following conditions.
If a = 0, then GCD (a, b) = b as GCD (0, b) = b.
If b = 0, then GCD (a, b) = a as GCD (a, 0) = a.
If both a≠0 and b≠0, we write 'a' in quotient remainder form (a = b×q + r) where q is the quotient and r is the remainder, and a>b.
Finding Common Divisors Method
In this method, we will find the common divisors for the two positive integers a and b then we will take out the common divisor for the two integer common divisors.
Look into the guidelines that are given below to calculate the GCD of any two positive integers easily. We are going to provide you with steps for all four methods that we have to find the GCD.
Prime Factorisation Method.
Take the value that was given in the problem.
Find the prime factors for the two positive integers.
Then, take out common prime factors and multiply them.
The result that you get is the greatest common divisor.
LCM Method
Take any two positive integer values.
Then you need to apply the formula, i.e., GCD (a,b) = [a x b] /[LCM(a,b)].
Now, you need to find the LCM for two positive integers and then find a product of a,b.
Finally, substitute the values in the formula and simplify it.
The result that you got is the GCD of two numbers .
Euclid's Algorithm Method
Note down the value that was taken from the problem.
If a = 0, then GCD (a, b) = b as GCD (0, b) = b.
If b = 0, then GCD (a, b) = a as GCD (a, 0) = a.
If both a≠0 and b≠0, we write 'a' in quotient remainder form (a = b×q + r) where q is the quotient and r is the remainder, and a>b.
Find the GCD (b, r) as GCD (b, r) = GCD (a, b)
Repeat the process until you get the remainder of Zero.
When the remainder is zero, the divisor at that stage is called GCD.
Finding Common Divisors Method
Let us take any two positive integers (a,b).
Write the divisors for the two positive integers a and b.
Now list out the divisors and take out the highest common divisor.
That common divisor is GCD.
Question :
How to Find the GCD of 2, 4?
Solution :
Given, that GCD(2,4)
By the method of prime factorization
GCD(2,4)
2 = 1 x 2
4 = 2 x 2
GCD(2,4) = 2.
(or)
By the Method of LCM
Formula,
GCD (a,b) = [a x b] /[LCM(a,b)]
LCM(2,4) = 4
Product of 2,4 is = 2x4 = 8.
GCD (2,4) = 8 / 4 = 2
(or)
By the Method of Common divisors
Divisor of 2 = 1,2
The highest Common Divisor of 2,4 is 2.
GCD(2,4) = 2
(or)
By using Euclids Algorithm,
Here, a = 2, b = 4
a≠0 and b≠0
According to Euclid's algorithm a>b.
As here, a < b we cannot perform the Euclid algorithm.
Look into our other maths calculator concepts on Roundingcalculator.Guru website. Use them and work easily.
1. What is the GCD(3,4)?
GCD of(3,4) is 1.
2. How to use this greatest common divisor calculator?
Simply, you need to give the inputs in the input field and then click on the calculate button. So that you will get the answers easily.
3. Find the GCD of 1 and 2 using the LCM method?
In the LCM method, the formula is
GCD (a,b) = [a x b] /[LCM(a,b)]
LCM(1,2) = 2
a x b = 1 x 2 = 2
= 2 /2 = 1.