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Greatest Common Divisor (GCD) Calculator Description


The largest positive number that divides a given group of positive integers evenly is referred to as the greatest common divisor (GCD). Other names for it include the greatest common factor (GCF) and the highest common factor (HCF). 


The biggest number that divides two numbers is said to be their greatest common divisor, or GCD for short. For instance, since 5 can be used to divide both 20 and 15 and no other number can do the same, So it is the greatest common factor of these numbers. The idea can be easily applied to sets of more than two numbers: the largest number that divides each number in a set of numbers is known as the GCD.

The GCD is used in a variety of number theory applications, particularly modular arithmetic and thus encryption algorithms such as RSA. Additionally, it is employed for less complex tasks like fractional simplification. Due to its importance to number theory, the GCD is a fundamental idea, and as a result, numerous algorithms have been developed to quickly compute it.

What is Greatest Common Divisor?

The greatest positive number that is a common factor of both the positive integers (a, b) is what is known as the greatest common divisor for a pair of positive integers (a, b). Since 1 is always the least positive integer that any two numbers have in common, the GCD of any two integers is never negative or zero. To find the greatest common divisor of two numbers, use one of two methods given below:

  • By identifying the common divisors
  • Euclid's algorithm is used.

The formula for calculating Greatest Common Divisor (GCD) is

GCD(a,b) =
|a . b| / LCM(a,b)

Example of Calculations:

Number: (34,56)

GCD(a,b) =
|34 x 56| / LCM(34,56)
= 2

How Do You Determine the Greatest Common Divisor?

The steps listed below are used to determine the greatest common divisor for a set of two positive integers (a, b):

  • Writing the divisors of mentioned positive integer "a." at first
  • Writing the divisors of mentioned positive integer "b." at second
  • Enlisting the common divisors of both "a" and "b".
  • Find the divisor that has the highest value among "a" and "b" in step four.

How to calculate Greatest Common Divisor (GCD) with a calculator?

  • You need to enter the number seperated by commas whose greatest common factor (GCD) you want to find.
  • Click on submit, the results of "Greatest Common Divisor (GCD)" will automatically appear below.

More Calculation (Examples of greatest common divisor)

  • Greatest Common Divisor Example 1:
  • Number: 21,7,28

    GCD =
    |21 x 7 x 28| / LCM(21, 7, 28)
    = 7

  • Greatest Common Divisor Example 2:
  • Number: 28,8,32,56

    GCD =
    |28 x 8 x 32 x 56| / LCM(28,8,32,56)
    = 4

  • Greatest Common Divisor Example 3:
  • Number: 58,24

    GCD =
    |58 x 24| / LCM(58,24)
    = 2
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