Calculate Gcd of N Numbers

What is GCD?

The greatest common divisor (GCD) of a set of integers is the largest positive integer that divides each of the integers without leaving a remainder. For example, the GCD of 8 and 12 is 4, since 4 is the largest number that divides both 8 and 12 without a remainder.

GCD is also known as the greatest common factor (GCF) and is often used in number theory and algebra. It is a fundamental concept in mathematics with applications in various fields.

How to Calculate GCD of N Numbers

Calculating the GCD of multiple numbers involves finding the largest number that divides all of them without leaving a remainder. Here's a step-by-step method to calculate the GCD of N numbers:

1. Start with the first two numbers and find their GCD using the Euclidean algorithm.
2. Take the result from step 1 and find its GCD with the next number in the list.
3. Repeat this process until you have found the GCD of all numbers in the list.

The Euclidean algorithm is an efficient method for computing the GCD of two numbers. It works by repeatedly replacing the larger number with the remainder of dividing the larger number by the smaller number until one of the numbers becomes zero. The non-zero number at this point is the GCD.

Example Calculation

Let's calculate the GCD of the numbers 12, 18, and 24.

1. First, find the GCD of 12 and 18 using the Euclidean algorithm:
   • 18 ÷ 12 = 1 with a remainder of 6
   • Now find GCD(12, 6): 12 ÷ 6 = 2 with a remainder of 0
   • The GCD of 12 and 18 is 6
2. Next, find the GCD of the result (6) with the next number (24):
   • 24 ÷ 6 = 4 with a remainder of 0
   • The GCD of 6 and 24 is 6

The GCD of 12, 18, and 24 is 6.