Need to find the greatest common divisor of two or more numbers? Our free GCD Calculator makes it quick and easy. Enter your numbers and get the greatest common divisor instantly. You can also add more numbers when you need to solve a larger calculation.
GCD Calculator
How to Use the GCD Calculator
Using the GCD Calculator is easy. Enter two or more positive whole numbers and click Calculate GCD.
If you need to calculate the GCD of more than two numbers, click + Add Number to add another input field. You can enter up to 10 numbers.
The calculator will show the greatest common divisor of all the numbers you entered. Click Clear to remove the values and start a new calculation.
What Is GCD?
GCD stands for Greatest Common Divisor. It is the largest positive whole number that can divide two or more numbers without leaving a remainder.
For example, the factors of 12 include 1, 2, 3, 4, 6, and 12.
The factors of 18 include 1, 2, 3, 6, 9, and 18.
The largest factor they have in common is 6, so the GCD of 12 and 18 is 6.
GCD Formula
There is more than one way to find the GCD. One of the most common methods is the Euclidean algorithm.
For two numbers, the process repeatedly divides the larger number by the smaller number and uses the remainder for the next step. When the remainder becomes zero, the last non-zero divisor is the GCD.
The calculator performs this process automatically, so you can get the answer without working through each step yourself.
GCD Calculator Examples
Example 1: GCD of 12 and 18
The common factors of 12 and 18 include 1, 2, 3, and 6.
The greatest one is 6.
GCD(12, 18) = 6
Example 2: GCD of 24 and 36
The factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The greatest common factor is 12.
GCD(24, 36) = 12
Example 3: GCD of 24, 36 and 48
When more than two numbers are involved, the same idea applies.
GCD(24, 36, 48) = 12
You can enter all three numbers into the calculator to get the result instantly.
GCD vs. LCM
GCD and LCM are related but they answer different questions.
GCD finds the largest number that divides the given numbers evenly.
LCM finds the smallest positive number that is a multiple of all the given numbers.
For example, for 12 and 18:
GCD = 6
LCM = 36
Both calculations are useful when working with factors, multiples, fractions, and other math problems.
Why Is GCD Useful?
GCD can make several types of math problems easier. It is often used when simplifying fractions, finding common factors, working with ratios, and solving problems involving divisibility.
For example, the fraction 24/36 can be simplified using their GCD.
The GCD of 24 and 36 is 12, so both numbers can be divided by 12:
24 ÷ 12 = 2
36 ÷ 12 = 3
Therefore:
24/36 = 2/3
GCD and Fractions
One of the most common uses of GCD is simplifying fractions.
To simplify a fraction, find the GCD of the numerator and denominator, then divide both by that number.
For example:
18/24
The GCD of 18 and 24 is 6.
Divide both numbers by 6:
18 ÷ 6 = 3
24 ÷ 6 = 4
So the simplified fraction is:
3/4
Frequently Asked Questions
What does GCD stand for?
GCD stands for Greatest Common Divisor. It is the largest positive whole number that divides two or more numbers without a remainder.
Is GCD the same as GCF?
Yes. GCD (Greatest Common Divisor) and GCF (Greatest Common Factor) generally refer to the same mathematical value.
Can I calculate the GCD of more than two numbers?
Yes. You can add additional numbers to the calculator and find the GCD of several numbers at once.
Can I enter decimal numbers?
No. This calculator is designed for positive whole numbers because GCD is normally defined using integers.
What is the GCD of two prime numbers?
If two different prime numbers are entered, their GCD is usually 1 because they have no common factor other than 1.
For example:
GCD(5, 7) = 1
Can GCD help simplify fractions?
Yes. Finding the GCD of the numerator and denominator is a simple way to reduce a fraction to its lowest terms.
Related Calculators
You may also find our LCM Calculator, Fraction Calculator, Ratio Calculator, Percentage Calculator, Average Calculator, Square Root Calculator, and Exponent Calculator useful for other math calculations.