RNGdle

Harshad Numbers

Divisible by the sum of their own digits.

What is it?

A Harshad number (from Sanskrit: "joy-giver") divides evenly by the sum of its digits. 18 is Harshad because 1+8=9 and 18÷9=2; 19 is not. Also called Niven numbers, they are a neat bridge between a number and its own digits.

  • Exact matches95,428
  • Odds1 in 10
  • Out of1,000,001

How it scores

Harshads are common — exactly 95,428 of them, roughly one number in ten — so the trait earns a modest score. Think of it as a small bonus that keeps an ordinary roll from feeling empty.

The formula: -log2(count / 1,000,001) bits per trait, capped at 20, summed with 0.5 decay per additional trait.

Highest-scoring harshad numbers

  1. 1,000,000score 34.5 · Mythic
  2. 1score 31.3 · Mythic
  3. 666score 31.2 · Mythic
  4. 777score 30.4 · Mythic
  5. 8score 27.9 · Mythic
  6. 2score 27.8 · Mythic
  7. 1,000score 27.7 · Mythic
  8. 100,000score 27.1 · Mythic
  9. 42score 26.4 · Mythic
  10. 420score 26.3 · Mythic

Related patterns

FAQ

Is every single-digit number Harshad?

Yes — any digit divides itself — but the trait still only earns a small score because so many numbers qualify.

What is a famous Harshad number?

1729, the taxicab number, is Harshad: 1+7+2+9 = 19 and 1729 = 19 × 91.

How many Harshad numbers are in the range?

Exactly 95,428 of them — roughly one in ten numbers. Exact counts are published on the how-it-works page.