GCD Calculator (Greatest Common Divisor)
GCD Calculator (Greatest Common Divisor)
Enter two or more numbers separated by commas. This finds the greatest common divisor (GCD) — also called the greatest common factor (GCF) — the largest number that divides evenly into all of them.
The calculation uses the Euclidean algorithm, one of the oldest algorithms still in everyday use: it repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder reaches zero, which converges far faster than checking every possible factor by hand. GCD is the tool behind simplifying fractions to lowest terms, and for three or more inputs the calculator finds the GCD of the first two, then combines that result with each remaining number in turn.
- How it's calculated: this uses the Euclidean algorithm, repeatedly replacing the larger number with the remainder of dividing it by the smaller number, until the remainder is zero.
- Works for any number of inputs: the GCD of a list of three or more numbers is found by taking the GCD of the first two, then finding the GCD of that result with the next number, and so on.
- Common uses: simplifying fractions to their lowest terms, splitting items into equal groups, and various scheduling and packing problems.
What's the difference between GCD and GCF?
Nothing — "greatest common divisor" (GCD) and "greatest common factor" (GCF) are two names for exactly the same concept, both referring to the largest number that evenly divides every number in a set.
What is the GCD of two numbers that share no common factors besides 1?
The GCD is 1 — such numbers are called "coprime" or "relatively prime," meaning they share no factors greater than 1.
GCD Calculator (Greatest Common Divisor)
Enter two or more numbers separated by commas. This finds the greatest common divisor (GCD) — also called the greatest common factor (GCF) — the largest number that divides evenly into all of them.
The calculation uses the Euclidean algorithm, one of the oldest algorithms still in everyday use: it repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder reaches zero, which converges far faster than checking every possible factor by hand. GCD is the tool behind simplifying fractions to lowest terms, and for three or more inputs the calculator finds the GCD of the first two, then combines that result with each remaining number in turn.
- How it's calculated: this uses the Euclidean algorithm, repeatedly replacing the larger number with the remainder of dividing it by the smaller number, until the remainder is zero.
- Works for any number of inputs: the GCD of a list of three or more numbers is found by taking the GCD of the first two, then finding the GCD of that result with the next number, and so on.
- Common uses: simplifying fractions to their lowest terms, splitting items into equal groups, and various scheduling and packing problems.
What's the difference between GCD and GCF?
Nothing — "greatest common divisor" (GCD) and "greatest common factor" (GCF) are two names for exactly the same concept, both referring to the largest number that evenly divides every number in a set.
What is the GCD of two numbers that share no common factors besides 1?
The GCD is 1 — such numbers are called "coprime" or "relatively prime," meaning they share no factors greater than 1.