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GCD Calculator
Find the greatest common divisor (GCD / GCF) of two integers. Enter your values, review the formula, and use the worked result as a quick check for everyday planning.
GCD Calculator
Find the greatest common divisor (GCD / GCF) of two integers.
Results
GCD
6
Formula: Use Euclidean algorithm repeatedly until remainder is 0
GCD Calculator: Greatest Common Divisor
Find the greatest common divisor (also called greatest common factor or highest common factor) of two integers using the Euclidean algorithm. Essential for simplifying fractions, ratio reduction, and number theory.
Formula
The Euclidean algorithm repeatedly replaces the larger number with the remainder when divided by the smaller, until the remainder is zero. The last non-zero remainder is the GCD.
Worked example
GCD of 84 and 18: 84÷18 = 4 rem 12; 18÷12 = 1 rem 6; 12÷6 = 2 rem 0. GCD = 6. Check: both 84 and 18 are divisible by 6, and no larger integer divides both.
Practical guidance
Simplifying fractions
To simplify 84/18, divide numerator and denominator by their GCD (6): 84÷6 = 14, 18÷6 = 3. The reduced fraction is 14/3. The GCD is the most efficient way to simplify fractions in a single step.
GCD of more than two numbers
This calculator finds GCD of two integers. For three or more numbers, find the GCD of the first two, then find the GCD of that result with the third number, and continue. GCD(a, b, c) = GCD(GCD(a, b), c).
Frequently asked questions
What formula does this calculator use?
Use Euclidean algorithm repeatedly until remainder is 0
Can I use decimal values?
Yes. Decimal inputs are supported for most calculators. Integer-based tools use rounded integer values where appropriate.
Is this calculator free?
Yes. CalcuNimble calculators are free and optimized for fast everyday use.