Floor Division Calculator

Enter a dividend and a divisor to compute the floor division result — the largest integer less than or equal to the exact quotient. The calculator returns the floor quotient, the remainder, and the regular decimal result side by side, so you can see exactly how floor division differs from standard division. Also try the Solution x (smallest non-negative) — Chinese Remainder Theorem Solver.

The number being divided

The number to divide by (cannot be zero)

Results

Floor Quotient ⌊Dividend ÷ Divisor⌋

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Remainder

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Exact Decimal Result

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Expression

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Frequently Asked Questions

What is floor division?

Floor division is a type of division where the result is rounded down to the nearest integer (whole number), regardless of whether the remainder is positive or negative. For example, 13 ÷ 4 = 3.25 in regular division, but the floor division result is 3. It is sometimes called 'integer division' or 'division with remainder'. See also our Factorial Calculator.

What is the difference between division and floor division?

Regular division returns a decimal (floating-point) result — for example, 7 ÷ 2 = 3.5. Floor division always returns the largest integer that is less than or equal to the exact result, so 7 ÷ 2 gives 3. The key difference becomes obvious when the division is not exact.

When do floor division and regular division give the same answer?

They give the same answer whenever the dividend is perfectly divisible by the divisor — meaning there is no remainder. For example, 8 ÷ 4 = 2 exactly, so both regular and floor division return 2.

Why is it called floor division?

The name comes from the mathematical 'floor function' ⌊x⌋, which maps any real number to the largest integer less than or equal to it. Imagine a number line where the 'floor' beneath a decimal value is the integer directly below it. You might also find our calculate Inverse Modulo useful.

How does floor division work with negative numbers?

With negative numbers, floor division still rounds toward negative infinity — not toward zero. For example, ⌊−7 ÷ 2⌋ = ⌊−3.5⌋ = −4, not −3. This differs from truncation (which rounds toward zero), so be careful when working with negatives.

What is the floor division of 9 ÷ 2?

9 ÷ 2 = 4.5 in regular division. Applying the floor function gives ⌊4.5⌋ = 4, so the floor division result is 4 with a remainder of 1.

How is floor division represented in programming languages?

In Python, the floor division operator is `//` (e.g., `9 // 2` returns `4`). In other languages like Java, C, and C++, integer division of two integers also truncates toward zero, but for negative numbers you may need `Math.floor()` explicitly to match true floor behavior.

What are real-life applications of floor division?

Floor division is used in many practical scenarios: splitting items evenly among groups (e.g., how many full boxes of 12 can you pack from 50 items?), calculating how many complete weeks fit in a number of days, time conversions (minutes to hours), and pagination in software (how many full pages does a list require).