GCD Calculator
Calculate the greatest common divisor of two or more positive integers using the Euclidean algorithm.
Category: Calculators
When to use?
Use it to reduce fractions, find the largest shared tile size for a grid, or check whether numbers are coprime.
How to use
- Enter two or more integers separated by commas, spaces, or line breaks.
- The Euclidean algorithm computes the GCD automatically.
- Review the result and use it for reduction or comparison.
Input Explanation
Enter at least two positive integers. Decimals and non-numeric values are ignored by validation.
Calculation Basis
The Euclidean algorithm repeats GCD(a, b) = GCD(b, a mod b) until the remainder becomes 0.
Usage Examples
- Reduce fractions - Divide a numerator and denominator by their GCD.
- Grid and tile planning - Find the largest square unit that evenly divides two dimensions.
Examples
- GCD(48, 36, 24) = 12
- GCD(100, 75) = 25, so 100/75 reduces to 4/3
- An 84 cm by 60 cm board can be divided into largest equal 12 cm squares
FAQ
What does coprime mean?
Two numbers are coprime when their GCD is 1, meaning they share no divisor greater than 1.
Does it support three or more numbers?
Yes. It applies GCD(GCD(a, b), c) repeatedly across the list.
Related Tools
- LCM Calculator - Calculate the least common multiple of two or more positive integers.
- Fraction ↔ Decimal Converter - Convert fractions to decimals and decimals to simplified fractions.
- Prime Number Checker - Check whether a natural number is prime and show its prime factorization when it is composite.
- Percentage Calculator - Find what percentage a part is of a whole, or calculate a percentage of a value.
- Discount Calculator - Enter the original price and discount rate to find the final price and the amount saved.
- Ratio Calculator - Simplify the ratio of two values, or solve for the unknown in a proportion.