Armstrong Number Checker
Check if numbers are Armstrong numbers (also called narcissistic numbers). Generate Armstrong numbers, explore their mathematical properties, and understand this fascinating concept in number theory.
Input Numbers
Enter numbers to check for Armstrong property
Armstrong Number Generator
Generate Armstrong numbers in a range
Examples
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Statistics
Results
Armstrong number check results
What is an Armstrong Number?
An Armstrong number (also known as a narcissistic number or perfect digital invariant) is a number that equals the sum of its own digits each raised to the power of the number of digits. For example, 153 is an Armstrong number because 1³ + 5³ + 3³ = 153.
3-Digit Example
153 = 1³ + 5³ + 3³
= 1 + 125 + 27 = 153 ✓
4-Digit Example
1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴
= 1 + 1296 + 81 + 256 ✓
Single Digit
9 = 9¹ = 9 ✓
All single digits are Armstrong
Non-Armstrong
123 ≠ 1³ + 2³ + 3³
123 ≠ 1 + 8 + 27 = 36 ✗
Mathematical Properties
Definition Formula
Known Armstrong Numbers
Interesting Facts
Applications & Use Cases
Number Theory Research
Study special number properties and patterns
Programming Practice
Common programming exercise for loops and powers
Educational Tool
Demonstrate powers, digit manipulation, and verification
Computational Mathematics
Computer-assisted mathematical discovery
Mathematical Puzzles
Brain teasers and mathematical recreation
Verification Systems
Test mathematical computation accuracy
Step-by-Step Examples
Example 1: Checking 153
Example 2: Checking 1634
Example 3: Checking 123 (Non-Armstrong)
Frequently Asked Questions
Why are there no 2-digit Armstrong numbers?
For 2-digit numbers, the maximum possible sum is 9² + 9² = 162, but the minimum 2-digit number is 10. No 2-digit number can equal the sum of its digits squared.
Are Armstrong numbers useful in real applications?
While not directly used in most practical applications, they're valuable for mathematical education, algorithm practice, and understanding number properties.
How many Armstrong numbers exist?
There are infinitely many Armstrong numbers, but they become extremely rare as the number of digits increases. The largest known has 39 digits.
What's the difference between Armstrong and narcissistic numbers?
They're the same thing! "Narcissistic number" is another name for Armstrong numbers, referring to how the number is "in love with itself" through the calculation.