GCD Calculator (Greatest Common Divisor)

Find the greatest common divisor (GCD) or greatest common factor (GCF) of two or more numbers using the Euclidean algorithm.

Result

Fill in the fields above, then press Calculate.

A GCD calculator finds the greatest common divisor (also called GCF or HCF) of two or more positive integers using the Euclidean algorithm and prime factorization.

Enter two or more positive integers, separated by commas or spaces. Click Calculate to find their greatest common divisor (GCD). The calculator shows the Euclidean algorithm steps and prime factorization, which can help when simplifying fractions.

Examples

GCD of 48 and 18

48 = 18×2 + 12; 18 = 12×1 + 6; 12 = 6×2 + 0. GCD is 6.

Frequently Asked Questions

What is the relationship between GCD and LCM?
For two numbers a and b, GCD(a, b) × LCM(a, b) = |a × b|.
Related Calculators
LCM Calculator
Prime Factorization Calculator
Factor Calculator
Fraction Calculator

Quick Tips

  • •Use the GCD to simplify fractions — divide both numerator and denominator by the result.
  • •Use the step-by-step breakdown to verify intermediate calculations.
  • •Remember the identity GCD(a,b) x LCM(a,b) = |a x b| to quickly find the LCM after computing the GCD.