gcd

Calculates the greatest common divisor (GCD) of two numbers using Euclidean algorithm. Computes the largest positive integer that divides both numbers without remainder. Supports both integers and decimal numbers by scaling decimals to integers with appropriate precision handling. Uses the efficient Euclidean algorithm for computation.

Signature

const gcd: (left: number, right: number) => number

Parameters

Name	Type	Description
left	-	First number (integer or decimal)
right	-	Second number (integer or decimal)

Returns

Greatest common divisor of the two numbers

Examples

Integer GCD calculations

import { gcd } from '@winglet/common-utils';

console.log(gcd(12, 8)); // 4 (largest number dividing both 12 and 8)
console.log(gcd(48, 18)); // 6
console.log(gcd(15, 25)); // 5
console.log(gcd(17, 13)); // 1 (coprime numbers)
console.log(gcd(100, 50)); // 50

Decimal and edge case handling

// Decimal numbers (scaled to integers)
console.log(gcd(1.2, 0.8)); // 0.4 (GCD of scaled integers, then scaled back)
console.log(gcd(2.5, 1.5)); // 0.5

// Edge cases
console.log(gcd(0, 5)); // 5 (GCD with zero)
console.log(gcd(7, 0)); // 7 (GCD with zero)
console.log(gcd(0, 0)); // 0 (by convention)
console.log(gcd(-12, 8)); // 4 (absolute values used)

Playground

import { gcd } from '@winglet/common-utils';

console.log(gcd(12, 8)); // 4 (largest number dividing both 12 and 8)
console.log(gcd(48, 18)); // 6
console.log(gcd(15, 25)); // 5
console.log(gcd(17, 13)); // 1 (coprime numbers)
console.log(gcd(100, 50)); // 50

Notes

Mathematical Properties:

• gcd(a, 0) = |a| for any non-zero a
• gcd(0, 0) = 0 by convention
• gcd(a, b) = gcd(b, a) (commutative)
• gcd(a, b) = gcd(|a|, |b|) (sign independent)
• Always returns a non-negative result

Use Cases:

• Simplifying fractions to lowest terms
• Finding common denominators in fraction arithmetic
• Cryptographic algorithms (RSA key generation)
• Number theory and mathematical proofs
• Optimization problems requiring common factors
• Periodic pattern analysis and frequency calculations

Performance: O(log(min(a, b))) time complexity using Euclidean algorithm. For decimal inputs, includes O(1) scaling operations. Space complexity is O(1).