Modulo Division: Divide with Remainder

Name: Modulo Division: Divide with Remainder
Author: Jürgen Kummer

Calculator for dividing a larger number by a smaller one, calculating how many times the smaller number fits into the larger number and for the indivisible remainder, the modulo. If the larger value is divisible by the smaller value, the remainder is zero; otherwise, the remainder is a positiv integer smaller than the larger value. The integer result is always the result of dividing the larger value by the smaller value, rounded down. The division with remainder is also called Euclidean division.
Please enter two positive numbers, the integer result and the remainder will be calculated and the equation for it will be shown.

Example: 7 : 3 = 2 remainder 1. The three fits into the seven twice, two times three is six, the remainder is seven minus six, i.e. one.

Division with remainder is often the first division method children learn in school. Calculating with decimals is usually learned afterward. One reason for this is certainly that division with remainder is easier; you can complete such a task more quickly. But even if you already know how to calculate with decimals, or are able or allowed to use a calculator, division with remainder is still required for other applications. Often, the remainder is the more important result than the integer divisor. The remainder is called modulo, and the operation that produces it as a result is called modulo division.
Modulo division is often used in computer science, and many programming languages use the percent sign % or the command mod for this purpose. Entering 5 % 3 or 5 mod 3 in a computer program therefore produces the result 2. Using this method, numbers can be ordered into x sets with little effort using modulo division by x. For example, modulo division by 2 produces one set of even numbers (remainder 0) and one set of odd numbers (remainder 1).

Last updated on 07/01/2025. Author: Jürgen Kummer

Larger value:
Smaller value:
Integer result:
Remainder (modulo):