Remainder Calculator

Remainder – Quick Cheat Sheet

Inputs: integers a (dividend) and b (divisor), with b ≠ 0.
Quotient: q = intdiv(a, b) (truncates toward zero in PHP).
Remainder: r = a % b (in PHP, r has the same sign as a).
Identity: a = q × b + r always holds for PHP’s intdiv and %.
Negatives: e.g., -17 % 5 = -2 in PHP (since the remainder follows the sign of a).
Euclidean remainder (FYI): some texts define a non-negative remainder: r_E = ((a % b) + |b|) % |b|.

Notes & edge cases

Division by zero is invalid; set b to a non-zero integer.
For very large integers, results follow PHP’s integer range (usually 64-bit on modern builds).
When comparing with other languages, check their remainder semantics—many use truncation toward zero but some define Euclidean remainders.