The Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder

Usage:

• reducing fractions to their simplest form
• performing division in modular arithmetic
• Computations using this algorithm form part of the cryptographic protocols that are used to secure internet communications, and in methods for breaking these cryptosystems by factoring large composite numbers
• solve Diophantine equations, such as finding numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers.
• a basic tool for proving theorems in number theory such as Lagrange’s four-square theorem
• the uniqueness of prime factorizations

Pseudocode

function gcd(a, b)
    while b ≠ 0
        t := b
        b := a mod b
        a := t
    return a

Swift Implementation

func gcd(_ a: Int, _ b: Int) -> Int {
	var t = 0
	var a = a
	var b = b
	while b != 0 {
		t = a
		a = b
		b = t%b
	}
	return a
}

References

• https://en.wikipedia.org/wiki/Euclidean_algorithm