GuideHarshad
Harshad Numbers
A Harshad number (also called a Niven number) is a positive integer divisible by the sum of its decimal digits. Example: 18, because 1+8 = 9 and 18 ÷ 9 = 2.
Formula
digitSum(n) > 0 and n ≡ 0 (mod digitSum(n)).
How to check
Sum the digits of n. If that sum is positive and divides n with no remainder, n is Harshad.
Example
198
198 → 1+9+8 = 18, and 198 ÷ 18 = 11, so 198 is Harshad. 197 → 1+9+7 = 17, and 197 is not divisible by 17.
Look up EP for this number in the calculator.
In RNGdle
Harshad numbers are common enough to show up often, but still a clean pattern signal. RNGdle awards the Harshad Number badge when the digit-sum rule holds.
- Harshad Number — Divisible by the sum of its own digits. (+1,048 EP)
Examples across the range
95,428 total · 36 samples spaced from low to high.
127,78355,56683,340111,114138,898166,671194,454222,225250,002277,797305,559333,342361,116388,892416,691444,452472,230500,004527,790555,584583,362611,118638,894666,684694,462722,232750,006777,788805,568833,352861,120888,912916,674944,460972,240
FAQ
- What are Harshad numbers?
- Harshad numbers are integers divisible by the sum of their own digits. They are also known as Niven numbers.
- Is 0 a Harshad number?
- Under RNGdle’s rule the digit sum must be > 0, so 0 is not treated as Harshad.
- Does RNGdle score Harshad numbers?
- Yes. Rolls divisible by their digit sum earn the Harshad Number badge.