gcd(1071, 462)
= 21
The shared factor can be found without listing every divisor.
Greatest Common Divisor Calculator
Find the exact GCD of two large integers. Simplify ratios and test common factors without rounding.
How this calculation works
When at least one input is nonzero, the greatest common divisor is the largest positive integer dividing both values. Euclid’s algorithm repeatedly replaces a pair with the divisor and remainder until the remainder becomes zero. This tool defines GCD(0, 0) as zero.
Inputs and accuracy
Enter two whole numbers. Signs do not make the returned GCD negative. GCD(a, 0) equals the absolute value of a, and this calculator uses GCD(0, 0) = 0.
When to use it
Reduce fractions by dividing the numerator and denominator by their GCD, compare shared factors, or check whether two integers are coprime when their GCD is one.
Worked examples
gcd(-48, 18)
= 6
Negative inputs still produce a non-negative GCD.
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