Number Tools

GCD Calculator

Calculate the Greatest Common Divisor of two or more numbers.

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Enter numbers (comma or space separated)

Enter at least 2 numbers to compute the GCD...

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About GCD Calculator

The GCD Calculator computes the Greatest Common Divisor (also called Greatest Common Factor) of two or more integers. The GCD is the largest positive integer that divides all the given numbers without a remainder. For example, GCD(12, 18) = 6, because 6 is the largest number that divides both 12 and 18 evenly.

Students use this tool in number theory and algebra courses to simplify fractions, find common factors, and solve Diophantine equations. The GCD is essential for reducing fractions to their lowest terms — divide both numerator and denominator by their GCD.

Developers encounter GCD in cryptography (RSA key generation), modular arithmetic, and algorithm design. The Euclidean algorithm used by this tool is one of the oldest known algorithms, dating back to ancient Greece, and remains an efficient method for computing GCD.

The calculator accepts two or more integers separated by commas or spaces. It uses the Euclidean algorithm iteratively, computing the GCD of the first two numbers, then computing the GCD of that result with the next number, and so on. Negative inputs are handled by using their absolute values.

All computation happens locally in your browser. No data is uploaded, stored, or transmitted. The tool is free, requires no registration, and has no usage limits.

How to Use GCD Calculator

Enter two or more integers separated by commas or spaces.

The GCD appears instantly below.

Click Copy to copy the result to your clipboard.

Negative numbers are handled using their absolute values.

Key Benefits

Instant Calculation: GCD appears as you type.

Multiple Numbers: Supports two or more integers at once.

Euclidean Algorithm: Uses the efficient classical method.

Copy to Clipboard: One click to grab the result.

Private & Free: All processing is local, no cost, no signup.

Common Use Cases

Simplifying the fraction 12/18: GCD(12, 18) = 6 → 12÷6/18÷6 = 2/3 — the fraction in lowest terms.

Finding common factors of 24 and 36: GCD(24, 36) = 12 — both numbers share factors 1, 2, 3, 4, 6, and 12.

RSA cryptography: GCD(e, φ(n)) = 1 is required for the public key exponent e — the GCD must be 1 (coprime) for RSA to work.

Simplifying 84/120: GCD(84, 120) = 12 → 84÷12/120÷12 = 7/10 — reducing a fraction to its simplest form.

Finding GCD of three numbers: GCD(48, 72, 120) = 24 — the largest number dividing all three without remainder.

Frequently Asked Questions

How many numbers can I enter?

The tool accepts two or more integers. Enter them separated by commas or spaces.

How are negative numbers handled?

The GCD is always positive. The tool uses the absolute values of negative inputs, so GCD(-12, 18) = 6.

What algorithm does the tool use?

It uses the Euclidean algorithm, an efficient method that repeatedly replaces the larger number by the remainder of dividing the two numbers.

Is the GCD Calculator free?

Yes, it is completely free with no registration required.

Tips & Best Practices

The Euclidean algorithm computes GCD efficiently: GCD(a, b) = GCD(b, a mod b), repeating until the remainder is 0.

GCD is always positive — for negative inputs, the tool uses absolute values: GCD(-12, 18) = GCD(12, 18) = 6.

If GCD(a, b) = 1, the numbers are 'coprime' or 'relatively prime' — they share no common factors other than 1.

To simplify a fraction a/b, divide both by GCD(a, b) — e.g., GCD(12, 18) = 6, so 12/18 simplifies to 2/3.

The LCM (Least Common Multiple) is related: LCM(a, b) = (a × b) / GCD(a, b) — use the LCM Calculator for this.

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