Number Theory
Euler's Totient Function - Number Theory
Learn the euler's totient function with examples, step-by-step guide, and calculator tools. Count of integers coprime to n
The euler's totient function is a fundamental concept in number theory. Count of integers coprime to n. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[\phi(n) = n\prod_{p|n}\left(1 - \frac{1}{p}\right)\]
Variables
φ(n)
Totient function
p
Prime divisors of n
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: [] → φ(12) = 12×(1-1/2)×(1-1/3) = 12×1/2×2/3 = 4
Example 2
Example 2: 4
Frequently Asked Questions
What is the euler's totient function?
Count of integers coprime to n
How do I calculate euler's totient function?
Use the formula: \phi(n) = n\prod_{p|n}\left(1 - \frac{1}{p}\right). Follow the steps provided above.
What tools can help with euler's totient function?
We provide online calculators: calculator