A GCD Calculator helps you find the Greatest Common Divisor (also known as the Greatest Common Factor or HCF) of two or more numbers. The GCD is the largest positive integer that evenly divides all given numbers without leaving any remainder.
This calculator is especially useful in mathematics, engineering, computer science, and real-life tasks such as simplifying fractions, analyzing ratios, or dividing objects or groups evenly. Instead of manually checking all divisors of the numbers, the GCD calculator provides an accurate result instantly.
It belongs to the category of Mathematical Calculators, specifically for number theory and arithmetic problem-solving.
formula
Euclidean Algorithm Formula
To find the GCD of two numbers a and b:
GCD(a, b) = GCD(b, a mod b)
Repeat the process until b becomes 0. Then:
GCD(a, 0) = a
Step-by-step:
- Divide a by b
- Replace a with b, and b with a mod b
- Repeat until b = 0
- The final value of a is the GCD
This method is very fast and accurate, even for large numbers.
Most Common GCD Values Table (Reference Guide)
Here is a quick table for common pairs of numbers and their GCD. This table is useful for students, teachers, or anyone who needs quick access without doing manual calculations.
| Number A | Number B | GCD(A, B) |
|---|---|---|
| 12 | 8 | 4 |
| 18 | 24 | 6 |
| 60 | 48 | 12 |
| 100 | 25 | 25 |
| 81 | 27 | 27 |
| 35 | 21 | 7 |
| 14 | 49 | 7 |
| 45 | 10 | 5 |
| 22 | 8 | 2 |
| 99 | 66 | 33 |
This table helps save time for commonly used numbers, especially when simplifying ratios or fractions quickly.
Example
Let’s find the GCD of 48 and 18 using the Euclidean Algorithm:
Step 1:
a = 48, b = 18
48 mod 18 = 12
So, GCD(48, 18) = GCD(18, 12)
Step 2:
a = 18, b = 12
18 mod 12 = 6
So, GCD(18, 12) = GCD(12, 6)
Step 3:
a = 12, b = 6
12 mod 6 = 0
So, GCD(12, 6) = 6
Final Answer:
GCD(48, 18) = 6
This process works for any two non-negative integers and can also be extended for more than two numbers by applying the same logic repeatedly.
Most Common FAQs
GCD (Greatest Common Divisor) is the largest number that divides two numbers without a remainder. LCM (Least Common Multiple) is the smallest number that both numbers divide evenly into. They are different concepts but often used together in number theory.
Yes, you can. To find the GCD of three or more numbers, start by finding the GCD of the first two, then use that result with the next number, and so on. For example, GCD(24, 36, 60) = GCD(GCD(24, 36), 60).
Yes, GCD is always a non-negative number. Even if the input values are negative, the calculator considers their absolute values to compute the GCD.