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Instantly compute the remainder of a division operation (A mod B). Analyze the quotient step-by-step and safely handle standard programming modular arithmetic.
[Divisor × Quotient + Remainder] proofThe number being divided.
Cannot be 0.
The most common use case for modulo. If you modulo any integer by 2 (n % 2) and the remainder is 0, the number is even. If the remainder is 1, it's odd.
When iterating infinitely through a fixed array (like an image carousel), modulo ensures the index loops back to 0 cleanly instead of crashing.
Modulo is essential for stripping hours from minutes, or converting total seconds into a standard digital clock format by finding the remainder.
Modulo (or mod) returns the remainder after integer division. If you divide A by B, the modulo result tells you what is left after the largest possible whole-number multiple of B is removed from A.
This operation is foundational in computer science because it powers cyclic indexing, hashing, parity checks, clock math, cryptography, and bounded random generation. In short, modulo lets you keep values within a fixed range efficiently.
Developers, students, interview candidates, and competitive programmers use modulo constantly to avoid off-by-one bugs and control loops, buffers, and periodic events.
Dividend = Divisor x Quotient + Remainder
Remainder = Dividend - (Divisor x floor(Dividend / Divisor))
Modulo Notation: A mod B = R
Where A is the dividend, B is the divisor, and R is the remainder. In strict mathematical modular arithmetic, the remainder is usually non-negative and less than the divisor.
Input: 47 mod 2
47 / 2 = 23 remainder 1
Result: 1, so 47 is odd.
Items: 5, current index: 4
Next index: (4 + 1) mod 5
Result: 0, loop back to first slide.
Total seconds: 367
Seconds: 367 mod 60 = 7
Formatted time ends with :07.
Compare modulo behavior across common scenarios and language styles.
| Expression | Math / Python Style | JS / Java / C++ Style | Use Case Insight |
|---|---|---|---|
| 10 mod 3 | 1 | 1 | Standard positive modulo |
| 47 mod 2 | 1 | 1 | Odd/even validation |
| -5 mod 3 | 1 | -2 | Negative remainder trap |
| (index + 1) mod n | Wraps 0..n-1 | Wraps 0..n-1 | Carousel/array cycling |
A major gotcha for new developers involves using modulo with negative numbers across different programming ecosystems. Mathematics relies on Euclidean division where remainders are strictly non-negative. However, processor architectures led many compiled languages to use Truncated division instead.
Javascript, Java, C++, C#
The remainder takes the sign of the Dividend.
Python, Ruby, pure Math
The remainder takes the sign of the Divisor.
If you are writing JavaScript or C# and need mathematical "wrap-around" behavior (like going backwards in an array), you must write a safe modulo function:
function safeMod(n, m) {
// Solves the negative dividend bug
return ((n % m) + m) % m;
}Help new developers understand the modulo operator and avoid the negative remainder trap in JavaScript.
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