Greatest Common Division Calculator
(GCD, HCF, GCF)
Enter whole numbers separated by commas or spaces.
GCD Calculator
This Greatest Common Divisor (GCD) Calculator is a fast, modern tool that helps you instantly find the Greatest Common Divisor of two or more numbers, complete with clear step-by-step solutions. Whether you’re a student, teacher, programmer, or anyone needing quick and reliable number simplification, this calculator is designed for you.
Unlike other GCD calculators that rely on server requests, this one runs entirely in your browser. All calculations happen locally and instantly, so there’s no waiting, no internet dependency, and no privacy concerns — your data never leaves your device. The results update in real time, making it both efficient and secure. With a clean, responsive design, the interface is carefully optimized for both desktop and mobile users. The layout is simple yet visually appealing, with smart spacing and readable font sizes, ensuring a smooth experience across devices.
This tool was created to make GCD calculation more accessible, accurate, and enjoyable. We’re continuously improving it to offer the best possible experience — not just another calculator, but one people love to use. Try it once, and you’ll see why students and teachers prefer this tool: it doesn’t just solve problems, it teaches them. Start now—understand GCDs, not just calculate them.
This Greatest Common Factor Calculator also works as a solution for finding:
Greatest common factor (GCF)
Greatest common denominator (GCD)
Highest common factor (HCF)
Greatest common divisor (GCD)
How to Use
- Enter Numbers
Type/paste numbers like: 24, 36, 48 or 12 18 30 (separated by commas or spaces) - Get Instant Results
- See GCD value immediately
- Expand the solution section for details
- Learn the Logic
- Study factor lists and common divisors
- Understand the calculation process
What is the Greatest Common Division?
Greatest Common Divisor (GCD), also called Greatest Common Factor (GCF), of two or more whole numbers is the largest number that divides all of them exactly, with no remainder. For example, the GCD of 12, 18, and 24 is 6, because 6 is the largest number that divides all three without a remainder.
There are several methods to find the GCD, each useful in different contexts. Below are the most common methods, explained step by step, with examples ranging from very simple to more complex.
1. Listing All Factors (for Small Numbers)
This is the most straightforward method, best suited for small numbers.
How it works:
List all positive divisors (factors) of each number.
Identify the common factors.
The largest one is the GCD.
Example 1: Find the GCD of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
So, the GCD is 6.
Example 2: Find the GCD of 8 and 20.
Factors of 8: 1, 2, 4, 8
Factors of 20: 1, 2, 4, 5, 10, 20
Common factors: 1, 2, 4
Therefore, GCD = 4
This method becomes inefficient for larger numbers, so we usually turn to other strategies in such cases.
2. Prime Factorization Method
In this method, we break down each number into its prime factors and then multiply the common prime factors using their smallest exponents.
Steps:
Find the prime factorization of each number.
Identify the prime factors that are common to both numbers.
Multiply these common prime factors using the lowest powers.
Example 3: Find the GCD of 36 and 60.
Prime factorization of 36: 22 × 32
Prime factorization of 60: 22 × 3 × 5
Common prime factors: 22 and 3
GCD = 22 × 3 = 12
Example 4: (More Complex):
Find the GCD of 420 and 588.
420 = 22 × 3 × 5 × 7
588 = 22 × 3 × 72
Common prime factors: 22, 3, and 7
GCD = 22 × 3 × 7 = 84
3. Euclidean Algorithm (Fastest for Big Numbers)
The Euclidean Algorithm is an efficient and widely used method that works by repeatedly applying the division algorithm.
Steps:
Divide the larger number by the smaller number.
Replace the larger number with the smaller number, and the smaller number with the remainder.
Repeat the process until the remainder is 0.
The last non-zero remainder is the GCD.
Example 5: Find the GCD of 48 and 18.
48 ÷ 18 = 2 remainder 12 → GCD(18, 12)
18 ÷ 12 = 1 remainder 6 → GCD(12, 6)
12 ÷ 6 = 2 remainder 0 → GCD = 6
Example 6 (Larger Numbers):
Find the GCD of 252 and 105.
252 ÷ 105 = 2 remainder 42 → GCD(105, 42)
105 ÷ 42 = 2 remainder 21 → GCD(42, 21)
42 ÷ 21 = 2 remainder 0 → GCD = 21
This method is very efficient, even for very large numbers, and is often used in programming and algorithms.
4. Repeated Subtraction Method (Early Euclidean Idea)
This is a simplified, older version of the Euclidean Algorithm. Instead of dividing, you just keep subtracting the smaller number from the larger until they are equal.
Example 7: Find the GCD of 30 and 18.
30 − 18 = 12
18 − 12 = 6
12 − 6 = 6
6 − 6 = 0
So, GCD = 6
This method is easy to understand but slow for larger numbers or numbers that differ a lot in size.
5. GCD of Three or More Numbers
To find the GCD of more than two numbers, you can apply the GCD function repeatedly:
GCD(a, b, c) = GCD(GCD(a, b), c)
Example 8:
Find the GCD of 24, 60, and 36.
First, GCD(24, 60) = 12
Then, GCD(12, 36) = 12
So, the final GCD = 12
You can apply this idea to any number of integers.