Euclidean Division Calculator

The Euclidean Division division is also called division with remainder. a divided by b is c remainder d.

Example: 11 divided by 4 is 2 remainder 3.

a, b, c, d ∈ ℕ, which means all four numbers are natural numbers.

d is the result of the modulo division a mod b (also written a % b).

Please enter the numerator a and the denominator b. The integer quotient c and the integer remainder d will calculated. a=b*c+d.

Division with remainder is often the first "divide-by-calculation" learned at school. Such calculations also play a role later on. For example, the number of minutes in time is in the number range from 0 to 59, i.e. in a sexagesimal system. If you have 100 minutes and divide them by those 60, you get 1 remainder 40, which can easily be interpreted as one hour and forty minutes.
Modulo division, sometimes simply called modulo, is often used in programming when you are working in a limited number range. In this case, the integer quotient is often not of interest at all. If, for example, a loop is run through i times and something is to be done on every xth run, this can be solved with modulo division i % x (or i mod x).

Division with remainder can be extended to real numbers. This means that the numerator, denominator and remainder can be real numbers, the integer quotient remains a natural number; a, b, d ∈ ℝ, c ∈ ℕ. This calculation can also be done here, but only with a positive numerator and denominator and of course only with rational numbers, which can be entered here. Example: 25.8 divided by 2.3 is 7 remainder 2.7.
There is also polynomial division with remainder, which works in the same way in principle, but is more difficult to calculate. Depending on the complexity of the polynomial in the denominator, this can be very complex; of course, you don't have this problem with simple numbers.