GCD Calculator
Calculate Greatest Common Divisor
Frequently Asked Questions
What is the GCD and how is it calculated?
The Greatest Common Divisor (GCD) is the largest number that divides two or more numbers without a remainder. The calculator uses the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until it reaches zero.
What is the Euclidean algorithm for finding GCD?
To find GCD(48, 18): 48 ÷ 18 = 2 remainder 12, then 18 ÷ 12 = 1 remainder 6, then 12 ÷ 6 = 2 remainder 0. The last non-zero remainder is the GCD: 6. This method is efficient even for very large numbers.
How is GCD used to simplify fractions?
Divide both numerator and denominator by their GCD. For 24/36: GCD(24,36) = 12, so 24/36 = 2/3. This gives the fraction in its simplest form.
Can I find the GCD of more than two numbers?
Yes. Find the GCD of the first two numbers, then find the GCD of that result with the third number, and so on. For example, GCD(12, 18, 24) = GCD(GCD(12,18), 24) = GCD(6, 24) = 6.
What is the relationship between GCD and LCM?
For any two numbers a and b: GCD(a,b) × LCM(a,b) = a × b. So LCM = (a × b) / GCD(a,b). For 12 and 18: GCD = 6, LCM = (12 × 18) / 6 = 36.