18Yes
- Check
18 % 9 == 0
Check Harshad Number in Python
What you’ll learn
- Harshad rule:
n % digit_sum(n) == 0for positiven. - Safe check that avoids division by zero and invalid inputs.
- Range scan for
1..20and a live preview.
Overview
A Harshad test is simple: compute digit sum once, then do one divisibility check.
Two programs
Single check for 18 and list in [1,20].
Live preview
Shows digit sum, remainder, and verdict.
Rigor
Positive-only definition and nonzero digit-sum guard.
Prerequisites
Loops, modulus, and integer division.
- Use
% 10and// 10to process decimal digits. - Know divisibility test with
n % s == 0.
What is a Harshad number?
A positive number n is Harshad if it is divisible by the sum of its digits.
Example: 18 has digit sum 9, and 18 % 9 == 0.
18Harshad
11Not
Rulen % s(n) == 0
Formal divisibility
Let s(n) be decimal digit sum. For n > 0, Harshad iff n ≡ 0 (mod s(n)).
20s(20)=2, so 20 mod 2 = 0.
Intuition
11No
- Check
11 % 2 != 0
Takeaway: all one-digit positive numbers are Harshad.
Live preview
Positive safe integers only.
Algorithm
Goal: check if positive n is divisible by its digit sum.
Compute digit sum
Loop through digits with % 10 and // 10.
Test divisibility
If sum > 0 and n % sum == 0, it is Harshad.
📜 Pseudocode
Pseudocode
function digit_sum_base10(n): // n >= 0
s = 0
while n > 0:
s += n mod 10
n = floor(n / 10)
return s
function is_harshad(n):
if n <= 0:
return false
s = digit_sum_base10(n)
if s == 0:
return false
return (n mod s) == 01Single value:
Single value: 18
Checks one number with safe guards and digit-sum helper.
python
def digit_sum_positive(n: int) -> int:
total = 0
while n > 0:
total += n % 10
n //= 10
return total
def is_harshad(number: int) -> bool:
if number <= 0:
return False
s = digit_sum_positive(number)
if s == 0:
return False
return number % s == 0
number = 18
if is_harshad(number):
print(f"{number} is a Harshad number.")
else:
print(f"{number} is not a Harshad number.")Explanation
For 18, digit sum is 9 and 18 is divisible by 9.
2Harshad numbers in
Harshad numbers in [1, 20]
Prints all Harshad numbers in the small interview range.
python
def digit_sum_positive(n: int) -> int:
total = 0
while n > 0:
total += n % 10
n //= 10
return total
def is_harshad(num: int) -> bool:
if num <= 0:
return False
s = digit_sum_positive(num)
return s != 0 and num % s == 0
print("Harshad numbers in the range 1 to 20:")
for i in range(1, 21):
if is_harshad(i):
print(i, end=" ")
print()Explanation
Numbers like 11 and 19 fail because they are not divisible by their digit sums.
Extensions
Large scans: use incremental digit-sum tricks for performance.
Other bases: replace base-10 extractor with base-b digits.
Interview: always mention positive-input and zero-sum guard.
❓ FAQ
A positive integer n is Harshad in base 10 if n is divisible by the sum of its decimal digits.
Yes. digit_sum(1)=1 and 1 % 1 = 0.
For n=0, digit sum becomes 0 and modulus by 0 is invalid. Standard definition uses positive n.
Yes, by using digits in that base and the same divisibility rule.
O(log10 n) digit operations plus one modulus.
Both use digit sums, but Harshad uses one sum, not repeated reduction.
🔄 Input / output examples
Change the value in Example 1 or bounds in Example 2.
| n | s(n) | Harshad? |
|---|---|---|
1 | 1 | Yes |
12 | 3 | Yes |
11 | 2 | No |
18 | 9 | Yes |
Edge cases and pitfalls
Validate positivity first to avoid invalid modulus.
Zero
n = 0
Not positive Harshad in this tutorial definition.
Negative
n < 0
Reject input unless you explicitly redefine behavior.
Base
Decimal default
Rule is base-dependent; this page uses base 10.
Large n
Big integers
Python supports them, but scan cost still grows with digit count.
⏱️ Time and space complexity
| Task | Time | Extra space |
|---|---|---|
| One value | O(log n) digits | O(1) |
Scan [1, N] | O(N log N) digit work | O(1) |
log n here means number of decimal digits.
Summary
- Rule: positive
nis Harshad ifn % digit_sum(n) == 0. - Code: compute sum, guard zero, then test divisibility.
- Watch-outs: reject
n <= 0and keep base explicit.
Did you know?
Harshad numbers are also called Niven numbers. The word “Harshad” comes from Sanskrit and means “joy-giver.”
About the author
8 people found this page helpful