GCD Calculator
Calculate Greatest Common Divisor (GCD) for any pair of integers.
GCD & LCM Calculator
About GCD Calculator
The Greatest Common Divisor (GCD / HCF) Step-by-Step Calculator computes the GCD of two or more integers using the Euclidean Algorithm, Prime Factorization, and Binary GCD with step-by-step mathematical proofs.
How to Use GCD Calculator
Step 1
Enter two or more integers separated by commas or spaces.
Step 2
Click "Calculate GCD".
Step 3
Review the step-by-step Euclidean division steps.
Step 4
Click "Copy Solution".
Practical Use Cases for GCD Calculator
Simplifying Fractions & Aspect Ratios
Find the GCD of video dimensions (e.g. $1920$ and $1080$, $\\text{GCD}=120$) to simplify them into their true aspect ratio ($16:9$).
Algebraic Number Theory & Cryptography
Compute modular multiplicative inverses and coprime numbers for RSA encryption key generation.
Input & Output Examples
Calculating GCD of 1920 and 1080
Numbers: 1920, 1080
GCD(1920, 1080) = 120 | Step 1: 1920 mod 1080 = 840 | Step 2: 1080 mod 840 = 240 | Step 3: 840 mod 240 = 120 | Step 4: 240 mod 120 = 0
Key Features & Performance
- ✓Calculates GCD (Highest Common Factor / HCF) for 2, 3, or an arbitrary list of numbers.
- ✓Displays full step-by-step Euclidean algorithm divisions ($a = bq + r$).
- ✓Supports BigInt arbitrary-precision arithmetic for massive 100+ digit numbers.
- ✓100% Client-Side calculation.
- ✓1-Click Copy GCD solution and step breakdown.
Key Terminology & Definitions
Greatest Common Divisor (GCD)
The largest positive integer that divides each of the given integers without leaving a remainder.
Euclidean Algorithm
An efficient method for computing the GCD based on the principle that the GCD of two numbers also divides their difference: $\\gcd(a, b) = \\gcd(b, a \\bmod b)$.