**Description:**

*eatest Common Divisor (GCD)*value of Two Numbers (the oldest Algorithm known, it appeared in Euclid’s Elements around 300 BC).

**GCD Value: -**

**Is the Largest number dividing the both numbers**

**Justification:**

**Step 1:**

**About Euclidean Algorithm**

*Possibility*

**#1:**

**Our aim is to find**

*GCD (a, b)*of two numbers

**a**and

**b.**

**Suppose**

**a**is smaller than

**b…..**

**b**by

**a**,

*if*we get

*reminder*

**zero**then …..We done it….

*B’coz***b**is multiple of

**a**.

**NOT**then again divide the

*Divisor**by*until we get reminder equal to

**Reminder****zero.**

**Last Non-Zero**reminder is the

*GCD*value of

**a**and

**b.**

**Step 2:**

**, we mention only one possibility of Euclidean Algorithm, but there are two more possibilities to find GCD Value between two numbers.**

*Step 1**Possibility*

**#2:**a == b

**[a**exactly equal to

**b]**

*Possibility*

**#3:**a > b

**[a**greater than

**b]**

**possibilities**

*Three***The Code:**

**1.**Accept two numbers from User. Declare the variable

**= 1.**

*reminder**Listing 1*

**2.**The Code for

*Possibility #1*(a < b)

*Listing 2*

**3.**The Code for

*Possibility #2*(a == b) &

*Possibility #3*(a > b)

*Listing 3*

**4.**Now execute the

*Application*and see the result (

*Figure 1)*.

**Intended Result:**

*Figure*

*1*

**Summary:**

**For writing the code here I used the C# Language.**

*The Euclidean Algorithm.*