GCD Calculator
Find the greatest common divisor, also called the greatest common factor or highest common factor.
GCD calculator
- Step 1Apply the Euclidean algorithm
48 ÷ 18 = 2 remainder 12 - Step 2Apply the Euclidean algorithm
18 ÷ 12 = 1 remainder 6 - Step 3Apply the Euclidean algorithm
12 ÷ 6 = 2 remainder 0
- Numbers
- 48, 18
- Greatest Common Divisor
- 6
Common GCD Problems
Simplifying Fractions
Reduce a fraction by dividing both terms by their GCD.
18/24 → GCD = 6 → (18 ÷ 6)/(24 ÷ 6) = 3/4Reducing Ratios
Simplify both parts of a ratio with their shared divisor.
12:18 → GCD = 6 → 12 ÷ 6 : 18 ÷ 6 = 2:3Equal Size Groups
24 apples and 36 oranges form 12 identical groups without leftovers.
Each group contains 2 apples and 3 orangesEqual Measurement Groups
A 240 by 360 rectangle can be divided into equal squares.
Maximum square side length = 120Formula
GCD
The largest positive integer that divides every number without remainderEuclidean Algorithm
gcd(a, 0) = |a|; gcd(a, b) = gcd(b, a mod b)Multiple Values
gcd(a, b, c) = gcd(gcd(a, b), c)Examples
GCD of 48 and 18
GCD(48, 18) = 6GCD of three integers
GCD(24, 36, 48) = 12GCD when one number divides another
GCD(81, 27) = 27GCD with zero
GCD(0, 24) = 24GCD with a negative integer
GCD(-48, 18) = 6Related Calculators
Frequently Asked Questions
What is the difference between GCD, GCF, and HCF?
There is no mathematical difference. GCD, greatest common factor, and highest common factor are names for the same value.
How do you calculate the GCD of two numbers?
Use the Euclidean algorithm: repeatedly replace the pair with the divisor and remainder until the remainder is zero.
Can the GCD be calculated for more than two numbers?
Yes. Find the GCD of the first pair, then combine that result with each remaining integer in order.
What is the GCD of 0 and a positive integer?
The GCD of zero and a positive integer is the positive integer. The GCD is undefined when every input value is zero.
How is GCD used to simplify fractions and ratios?
Divide every term by the GCD. For example, dividing 18 and 24 by 6 reduces 18/24 to 3/4.