You enter a dividend (A) and a divisor (B). The tool computes the floor quotient Q = floor(A ÷ B) and the remainder R = A mod B using JavaScript's built-in modulo operator. It then displays the full identity A = B × Q + R. It assumes integer inputs and uses truncated division consistent with most programming languages.
Division by zero is undefined in mathematics and produces no result. This calculator returns a dash when B is zero, since there is no valid quotient or remainder.
Yes, but the sign of the remainder depends on the language or tool. JavaScript's % operator keeps the sign of the dividend, so −7 % 3 = −1. Other languages (Python, for example) keep the sign of the divisor.
Common uses include checking divisibility (R = 0 means divisible), cycling through arrays or circular buffers, clock arithmetic (hours mod 12), and alternating row colors in a table (row mod 2).
For positive numbers, yes. For negative numbers, "modulo" and "remainder" can differ depending on convention. This calculator uses JavaScript's remainder operator, which matches the C/Java convention.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.