Number Theory
Greatest Common Divisor - Number Theory
Learn the greatest common divisor with examples, step-by-step guide, and calculator tools. Euclidean algorithm for GCD
The greatest common divisor is a fundamental concept in number theory. Euclidean algorithm for GCD. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[\gcd(a,b) = \gcd(b, a \bmod b)\]
Variables
gcd(a,b)
Greatest common divisor
a mod b
Remainder of a/b
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → gcd(48, 18) = gcd(18, 12) = gcd(12, 6) = 6
Example 2
Example 2: 6
Frequently Asked Questions
What is the greatest common divisor?
Euclidean algorithm for GCD
How do I calculate greatest common divisor?
Use the formula: \gcd(a,b) = \gcd(b, a \bmod b). Follow the steps provided above.
What tools can help with greatest common divisor?
We provide online calculators: calculator