Niven Number Checker

n ÷ digitSum(n) = integer

CalculatorsFreeNo Signup
4.4(569 reviews)
All Tools

Loading tool...

About Niven Number Checker

A Niven (Harshad) number checker testing if n is divisible by its digit sum. Shows quotient, consecutive Niven runs, multiple Niven check, and counts in range. All numbers up to 100 that are Niven. Client-side.

Niven Number Checker Features

  • Niven check
  • Digit sum
  • Quotient
  • Consecutive
  • Range count
Niven (Harshad) number: n divisible by sum of its digits. 18: 1+8=9, 18÷9=2 ✓. 21: 2+1=3, 21÷3=7 ✓. About 1/(d·4.5) of d-digit numbers are Niven. The first 20: 1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42.

How to Use

Enter n:

  • Niven?: Is digitSum(n)|n?
  • Quotient: n/digitSum(n)
  • Consecutive: Niven runs near n

Properties

  • All single digits are Niven
  • Density: ~log₁₀(n)/n × constant
  • Max consecutive: 20 (starting at n=10⁹+2)
  • Every Niven number has a multiple that is also Niven

Multiple Harshad

MHN: n such that n/s(n) is also Harshad, and so on. If this chain has length k, n is a k-Harshad number. Connected to Kaprekar and Moran numbers.

Step-by-Step Instructions

  1. 1Enter number.
  2. 2Check Niven.
  3. 3See digit sum.
  4. 4View quotient.
  5. 5Find nearby.

Niven Number Checker — Frequently Asked Questions

How common are Niven numbers?+

About N·ln(ln(N))/ln(N) Niven numbers below N. They thin out but never disappear. Among 1-digit: all 9. Among 2-digit: 33%. Among 3-digit: ~17%. The density decreases roughly as c/log(n).

What is the longest run of consecutive Niven numbers?+

At most 20 consecutive integers can all be Harshad numbers. The smallest such run of 20 starts at 10^(2·(10^18−1)/9). For practical ranges: runs of 7 are common, runs of 10+ are very rare.

What is a Moran number?+

A Harshad number n where n/s(n) is prime. Examples: 18/9=2 (prime), 21/3=7 (prime). Moran numbers are a subset of Harshad numbers. They provide a way to 'extract' primes from composite numbers.

More Calculators Tools

Explore all 639 other calculators tools available on Generatr

1-Sample Z-Test Calculator2-Sample Z-Test Calculator3D Surface Area CalculatorA/B Testing Significance CalculatorAbsolute Value CalculatorAbundant Number CheckerAccelerated Aging CalculatorAchromatic Number CalculatorAcyclic Chromatic Number CalculatorAdditive Persistence CalculatorAge CalculatorAging Test CalculatorAlbertson Index CalculatorAlgebraic Connectivity CalculatorAliquot Sequence CalculatorAliquot Sum CalculatorAlternating Series Test CalculatorAmicable Number FinderAnnuity CalculatorAPY CalculatorAquarium CO2 Drop CheckerArea CalculatorArea Under Curve CalculatorArithmetic Sequence CalculatorArmstrong Number CalculatorASCVD Risk CalculatorAspect Ratio CalculatorAtom Bond Connectivity CalculatorAugmented Eccentric Connectivity CalculatorAugmented Zagreb Index Calculator
View all 639 calculators tools
Share this tool: