Quotient and Remainder of a Division
Last Updated: June 7, 2026
Understanding the Problem
Division gives two pieces of information at once. The quotient is how many whole times the divisor fits into the dividend. The remainder is what is left over after taking out those whole copies.
Split 17 candies among 5 children equally: each child gets 3 candies, and 2 are left over. The quotient is 3, the remainder is 2, and the answer is [quotient, remainder].
The identity dividend = divisor * quotient + remainder ties them together. For the candy example, 5 * 3 + 2 = 17, the original dividend. This is the simplest way to confirm both answers are correct.
Key Constraints:
divisor != 0→ Division by zero is undefined, so the problem guarantees the divisor is never zero. You do not need to handle that case.-2^31 <= dividend, divisor <= 2^31 - 1→ Both inputs fit in a 32-bit signed integer, so the built-in division and modulo operators handle them directly without overflow concerns for the result.
Approach 1: Integer Division and Modulo
Intuition
Every language provides two operators that compute exactly what the problem asks, so there is no need to simulate division by repeated subtraction.
Integer division (/ in most languages, // in Python) keeps only the whole part and drops the fraction. For 17 / 5, the true value is 3.4, and integer division keeps 3. That is the quotient.
The modulo operator (%) returns the leftover. For 17 % 5, the result is 2, because 5 fits into 17 three times with 2 remaining. That is the remainder.
The answer is [dividend / divisor, dividend % divisor].
One detail: with negative numbers, languages disagree on the sign of the remainder. In Java, C++, C#, Go, Rust, JavaScript, and TypeScript, -17 % 5 gives -2 (the remainder takes the sign of the dividend), while Python gives 3 (the remainder takes the sign of the divisor). The identity dividend = divisor * quotient + remainder still holds in every language, but the exact pair of values differs. The examples here use non-negative operands so the quotient and remainder match across all of them.
Algorithm
- Compute the quotient using integer division:
quotient = dividend / divisor. - Compute the remainder using modulo:
remainder = dividend % divisor. - Return the two values together as an array
[quotient, remainder].
Example Walkthrough
Input: dividend = 17, divisor = 5
Integer division: 17 / 5 = 3 (we keep the whole part and drop the .4). The quotient is 3.
Modulo: 17 % 5 = 2, because 5 * 3 = 15, and 17 - 15 = 2. The remainder is 2.
Check the identity: divisor * quotient + remainder = 5 * 3 + 2 = 17, which equals the dividend. The answer is correct.
Code
- Time Complexity: O(1). The division and modulo operators are single arithmetic operations that run in constant time regardless of the input values.
- Space Complexity: O(1). We store two integers and return them in a fixed-size array, so the memory used does not grow with the input.