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Euclidean Algorithm

This program calculates the Greatest Common Denominator (GCD) of two integers. It is based on the Euclidean algorithm for finding the GCD.

Euclidean Algorithm to find the GCD of two integers
Basic Algorithm - Flow chart

This is the full Matlab program that follows the flow-chart above, without using the built-in 'gcd' instruction.

% Clears screen and deletes all the variables in the workspace
clear; clc

% Asks the user for input and takes only positive numbers into account
a = input('First number: ');
b = input(
'Second number: ');
a = abs(a);
b = abs(b);

% This is the real trick, normally performed a number of times
r = a - b*floor(a/b);

% Repeats the operation until updates of a equal updates of b
while r ~= 0
a = b;
b = r;
r = a - b*floor(a/b);

end

% Displays the result
GCD = b

Example 1:


Find the greatest common denominator of 18 and 50.

Run the algorithm above and enter data:

First number: 18
Second number: 50

GCD =
2


The built-in Matlab command 'gcd' also works on vectors. For example:

a = [50 150 20]
b = [18 115 5]

>> gcd(a,b)

ans =
2 5 5


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