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An Armstrong number (also called a narcissistic number) is a curious kind of number that equals the sum of its own digits, each raised to the power of the total digit count — 153 is the classic example. This checker tests any number against that definition and shows the full digit-power breakdown, with a full step-by-step solution.
How it works
Enter a number. The checker splits it into individual digits, raises each digit to the power of the total digit count, sums the results, and compares that sum back to the original number.
- Enter number.
- Click Calculate to see your results.
Examples
Checking 153
153 has 3 digits, and 1³ + 5³ + 3³ = 1 + 125 + 27 = 153 — so 153 is an Armstrong number.
Who should use it
- Verifying Armstrong number claims for a math or programming exercise.
- Exploring number theory curiosities like narcissistic numbers.
Industry applications
- Computer science and programming education
- Recreational mathematics and number theory
Advantages
- Gives an exact verdict along with the full digit-power sum for transparency.
- Works correctly for numbers of any digit count, not just 3-digit numbers.
Limitations
- Armstrong numbers become extremely rare as digit count grows, so most large numbers tested will not be Armstrong numbers.
Common mistakes to avoid
- Always raising digits to the power of 3, which only works correctly for 3-digit numbers — the power must match the actual digit count.
- Confusing Armstrong numbers with perfect numbers, which are a completely different concept based on divisors, not digit powers.
Best practices
- When exploring Armstrong numbers as a coding exercise, test single-digit, 3-digit, and 4+ digit numbers separately to confirm the digit-count power is handled correctly in each case.
Tips
- All single-digit numbers (0 through 9) are trivially Armstrong numbers, since any single digit raised to the power of 1 equals itself.