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Armstrong Number Checker – Narcissistic Test

Quick answer

An Armstrong number equals the sum of its digits each raised to the digit count: 153=1³+5³+3³.

  • Check 370, 371, 407, 1634 instantly.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the Armstrong Number Checker Works

n-digit number is Armstrong ⇔ n = Σ (digitᵏ), k = number of digits

An Armstrong (narcissistic) number equals the sum of its own digits each raised to the power of the digit count. For 3-digit numbers the power is 3: 153 → 1³+5³+3³ = 1+125+27 = 153 ✓, and its siblings 370, 371 and 407 complete the three-digit club. For 4-digit numbers the power is 4: 1634 → 1+1296+81+256 = 1634 ✓. The checker prints the digit-by-digit powers, their sum, and the verdict; single digits 1–9 are all trivially Armstrong (k = 1). The sequence is finite per digit-length and known to end at 39 digits (the largest is 115132219018763992565095597973971522401). Related curiosities appear too: 371 is also the sum of cubes of its digits, and 5 → 5¹ works but 10 → 1¹+0¹ = 1 fails.

  1. 1

    Enter a number

    Any positive integer such as 153

  2. 2

    Count the digits

    The exponent k equals the digit count (3 for 153)

  3. 3

    Raise and sum

    Each digitᵏ is computed and listed: 1, 125, 27

  4. 4

    Compare with the original

    Sum 153 equals the input → Armstrong

Use Cases

Programming Drills

The classic loop-and-power exercise in intro CS courses

Number Play

Hunt 3-digit members 153, 370, 371, 407

Interview Warm-ups

Digit manipulation with power sums in under 10 lines

Tips

  • 1

    The exponent is the digit count — 153 uses cubes, 1634 fourth powers

  • 2

    All single digits 1–9 are Armstrong numbers

  • 3

    370, 371 and 407 join 153 as the only 3-digit cases

Common Mistakes

  • Raising digits to a fixed power 3 regardless of digit count

  • Including 0 — it has one digit and 0¹ = 0, conventionally excluded

  • Summing the digits first and then raising the sum

  • Expecting many hits: only four exist below 10,000

FAQs

Is 153 an Armstrong number?

Yes: 1³+5³+3³ = 1+125+27 = 153.

What are the 3-digit Armstrong numbers?

153, 370, 371 and 407 — the only four.

Is 1634 narcissistic?

Yes, as a 4-digit case: 1⁴+6⁴+3⁴+4⁴ = 1+1296+81+256 = 1634.

Is 10 an Armstrong number?

No: 1¹+0¹ = 1 ≠ 10.

Do Armstrong numbers run out?

Yes — the largest has 39 digits; none exist beyond that length.