18 Harshad
- Check
18 % 9 == 0
Check Harshad Number in PHP
What you’ll learn
- The Harshad (Niven) rule in base 10:
ndividess(n), the sum of decimal digits. - A safe
is_harshadimplementation that avoids division by zero for invalid inputs. - A range scan for
1 ≤ n ≤ 20matching the reference output, plus a live preview.
Overview
Harshad numbers combine a digit walk with one divisibility test. They appear in recreational number theory and as quick loop exercises on interviews.
Two programs
18 and the 1–20 list from the reference.
Live preview
Positive safe integers; shows digit sum and remainder.
Rigor
n > 0, s(n) > 0 for the modulus, and clear base-10 scope.
Prerequisites
Integer remainder (%), loops, and if.
- Basic PHP syntax, loops, functions, and
echo. - Divisibility:
a % b == 0meansbdividesa(forb != 0).
What is a Harshad number?
A positive integer n is Harshad in base 10 if s(n) | n, where s(n) is the sum of the decimal digits of n.
For 18, digits sum to 9, and 18 = 9 · 2, so 18 is Harshad (the reference example).
18 s = 9
11 s = 2
Test n % s == 0
Formal divisibility
Write s(n) = ∑i di for decimal digits di. Then n is Harshad iff n ≡ 0 (mod s(n)) and s(n) > 0 (automatic for n > 0 in base 10).
20s(20) = 2 and 20 mod 2 = 0, so 20 appears in the small range list.
Intuition
11 Not
- Check
11 % 2 != 0
Takeaway: single-digit numbers are always Harshad in base 10 because s(n) = n.
Live preview
Positive integers in the JavaScript safe range.
Algorithm
Goal: decide whether n > 0 is divisible by the sum of its decimal digits.
Digit sum
Initialize s = 0. While n > 0, add n % 10 to s and divide n by 10. Keep a copy of the original n before the loop.
Divisibility
If s > 0 and original % s == 0, report Harshad.
📜 Pseudocode
Pseudocode
function digit_sum_base10(n): // assume 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
Same behavior as the reference (isHarshadNumber) with a safe zero guard to prevent division by zero.
php
<?php
function isHarshadNumber(int $number): bool
{
if ($number <= 0) {
return false;
}
$originalNumber = $number;
$sumOfDigits = 0;
while ($number > 0) {
$sumOfDigits += $number % 10;
$number = intdiv($number, 10);
}
if ($sumOfDigits === 0) {
return false;
}
return $originalNumber % $sumOfDigits === 0;
}
$number = 18;
echo isHarshadNumber($number)
? "$number is a Harshad number.\n"
: "$number is not a Harshad number.\n";
?>Explanation
For 18, the digit sum is 9. Since 18 % 9 == 0, the function returns true.
2Harshad numbers in
Harshad numbers in [1, 20]
Same listing as the reference: 1 2 3 4 5 6 7 8 9 10 12 18 20.
php
<?php
function isHarshadNumber(int $number): bool
{
if ($number <= 0) {
return false;
}
$sumOfDigits = 0;
$n = $number;
while ($n > 0) {
$sumOfDigits += $n % 10;
$n = intdiv($n, 10);
}
if ($sumOfDigits === 0) {
return false;
}
return $number % $sumOfDigits === 0;
}
$rangeStart = 1;
$rangeEnd = 20;
echo "Harshad numbers in the range $rangeStart to $rangeEnd:\n";
for ($i = $rangeStart; $i <= $rangeEnd; $i++) {
if (isHarshadNumber($i)) {
echo $i . " ";
}
}
echo "\n";
?>Explanation
11, 13, 14, 15, 16, 17, and 19 fail the final modulus test; the rest pass.
Extensions
Precompute sums. For scanning huge intervals, digit DP or incremental updates can amortize work; overkill for n ≤ 20.
Other bases. Generalize the digit extractor with radix b to test Harshad-b numbers.
Interview: mention n > 0 and never dividing by a zero digit sum.
❓ FAQ
A positive integer n is a Harshad (or Niven) number in base 10 if n is divisible by the sum of its decimal digits. Example: 18 has digit sum 9 and 18 is divisible by 9.
Yes. The digit sum of 1 is 1, and 1 is divisible by 1.
For n = 0 the usual digit loop yields sum 0, and n % 0 is undefined in PHP. The definition is for positive integers, so reject n <= 0 before dividing.
Yes. Replace decimal digits with base-b digits and use the same divisibility test. Base-10 Harshad numbers are the common interview default.
O(log10 n) digit operations to compute the digit sum, plus O(1) for the final modulus test.
The digit sum appears in digital root ideas, but Harshad only needs one sum, not iterated reduction to a single digit.
🔄 Input / output examples
Change number in Example 1 or the loop bound in Example 2.
| n | s(n) | Harshad? |
|---|---|---|
1 | 1 | Yes |
12 | 3 | Yes |
11 | 2 | No |
18 | 9 | Yes |
Edge cases and pitfalls
The reference logic assumes a positive number. Without guards, n == 0 yields s = 0 and % 0, which is undefined behavior in PHP.
Zero
n = 0
Not a positive Harshad number; reject before the modulus.
Negatives
n < 0
A while (n > 0) digit loop skips negatives in this form; this page keeps the standard positive-only definition.
Trailing zerosLarge
Large n
Digit sums stay small relative to n; overflow is rare unless you multiply partial results incorrectly.
Base
Radix
Clarify base 10 in APIs; other bases change both digits and the divisor.
⏱️ Time and space complexity
| Task | Time | Extra space |
|---|---|---|
One n | O(log n) decimal digits | O(1) |
Scan [1, N] | O(N log N) digit work total | O(1) |
Here log n means base-10 logarithm: proportional to the number of decimal digits of n.
Summary
- Rule: positive
nis Harshad iffn % digit_sum(n) == 0. - Code: preserve
original, accumulatesum, guardsum != 0. - Watch-outs:
n ≤ 0, base radix, and never dividing by a zero digit sum.
Did you know?
The same class of integers is often called Niven numbers in English-language sources (after Ivan Niven’s 1977 talk); Harshad comes from Sanskrit and means “joy-giver.”
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