Integer Division Remainder Calculator

Understanding Integer Division and Remainder

Integer division is a fundamental arithmetic operation that tells us how many times one number (the divisor) is completely contained within another number (the dividend), along with the remainder. The remainder is what's left over after performing integer division. For example, when you divide 17 by 5, the integer division result (quotient) is 3 because 5 fits into 17 three times completely (5 * 3 = 15). The remainder is 2 because 17 - 15 = 2.

In mathematical terms, if we divide an integer 'a' (dividend) by a non-zero integer 'b' (divisor), we get a quotient 'q' and a remainder 'r' such that: $$ a = b \times q + r $$, where $$ 0 ≤ r < |b| $$ Here, 'r' is the remainder we calculate using this tool. The remainder is always a non-negative integer and is less than the absolute value of the divisor. This operation is also known as the modulo operation, often represented as a mod b or a % b in programming.

This calculator is useful for various applications, from basic arithmetic to computer programming, cryptography, and more, wherever you need to find the leftover amount after division.