# 1. Introduction

The Greatest Common Divisor (GCD) of two integers is the largest integer that can divide both numbers without leaving a remainder. In this guide, we'll look into a Swift program to determine the GCD of two numbers using Euclid's algorithm.

# 2. Program Overview

We will start by defining the two numbers we want to find the GCD for. Then, using Euclid's algorithm, we'll iteratively calculate the GCD of the two numbers.

# 3. Code Program

``````// Define the two numbers
let num1 = 56
let num2 = 98

// Function to compute the GCD of two numbers using Euclid's algorithm
func gcd(_ a: Int, _ b: Int) -> Int {
if b == 0 {
return a
} else {
return gcd(b, a % b)
}
}

let result = gcd(num1, num2)
print("GCD of \(num1) and \(num2) is: \(result)")
``````

### Output:

```GCD of 56 and 98 is: 14
```

# 4. Step By Step Explanation

1. let num1 = 56 and let num2 = 98: We start by defining the two numbers for which we want to determine the GCD.

2. The function gcd calculates the Greatest Common Divisor of the two numbers using Euclid's algorithm. The logic behind this algorithm is that the GCD of two numbers (let's say a and b, where a > b) is the same as the GCD of b and a % b.

3. If b is 0, the GCD is a. Otherwise, we recursively call the gcd function with b and a % b as the new parameters.

4. After defining the gcd function, we call it with our two defined numbers as arguments and then print out the result.

Euclid's algorithm provides an efficient way to calculate the GCD, especially for larger numbers.