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Greatest Common Divisor (GCD) Calculator

Calculate the Greatest Common Divisor of the given numbers.

Result:

The GCD calculator allows you to find the largest positive integer that divides two or more numbers without leaving a remainder.

GCD is useful in various situations, such as simplifying fractions, finding equivalent fractions, determining common factors, simplifying ratios, and solving problems related to divisibility and modular arithmetic.

How to calculate GCD?

To calculate the GCD, there are several methods available, including Prime Factorization and the Euclidean algorithm.

If you want to calculate the GCD for multiple numbers, it is usually easiest to use a calculator.

Prime Factorization

  1. Write down the prime factorization of each number in the set.
  2. Identify the common prime factors among the numbers.
  3. Multiply the common prime factors together to obtain the prime factorization of the GCD.
Example #1: Finding the GCD of the numbers 12, 30, and 60:

Step 1: Prime factorize each number:

  • 12 = 2 * 2 * 3
  • 30 = 2 * 3 * 5
  • 60 = 2 * 2 * 3 * 5

Step 2: Identify the common prime factors:

The common prime factors are 2 and 3.

Step 3: Multiply the common prime factors together:

GCD = 2 * 3 = 6
Example #2: Finding the GCD of the numbers 18 and 27:

Step 1: Prime factorize each number:

  • 18 = 2 * 3 * 3
  • 27 = 3 * 3

Step 2: Identify the common prime factors:

The common prime factors are 3 and 3.

Step 3: Multiply the common prime factors together:

GCD = 3 * 3 = 9

Examples

Numbers GCD
10, 15, 25 5
12, 90 6
15, 45, 90 15
7, 17, 83 1
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