Floor Division Calculator

Floor division divides one number by another and rounds the quotient downward to the nearest integer. The word downward is important: the result moves toward negative infinity, not merely toward zero. For 17 divided by 5, the ordinary quotient is 3.4 and the floor quotient is 3. For -17 divided by 5, the ordinary quotient is -3.4 and the floor quotient is -4. This calculator applies that mathematical definition consistently to positive and negative inputs. Along with the quotient, the calculator reports a remainder that satisfies the division identity: dividend equals divisor times quotient plus remainder. After finding the floor quotient q, it computes the remainder r as dividend minus divisor times q. For 17 and 5, that produces q equal to 3 and r equal to 2. For -17 and 5, it produces q equal to -4 and r equal to 3. In both cases, substituting the displayed values reconstructs the original dividend exactly. Floor division appears frequently in programming. It is useful for splitting a total into complete groups, converting a flat array index into row and column coordinates, dividing elapsed seconds into whole minutes, paginating records, and implementing modular arithmetic. Languages do not all treat division of negative values the same way. Python's double-slash operator follows floor division, while truncating integer division in some other languages moves toward zero. That difference affects both quotient and remainder signs. The divisor must never be zero because division by zero has no finite mathematical result. Decimal inputs are allowed because the floor operation is defined for real quotients, although many everyday applications use integers. Floating-point arithmetic can have small representation limitations for long decimals, so use sensible precision when checking decimal identities. When the divisor is positive, the floor-division remainder is nonnegative and smaller than the divisor. With a negative divisor, the remainder is nonpositive and greater than the divisor. This sign behavior follows directly from choosing the quotient by flooring the real division result. The displayed identity makes it easy to verify every answer and distinguish floor division from truncation or ordinary rounded division.