RedCrab Math Tutorial

# Euclidean division

Euclidean division is the division of two integers, which produces a quotient and a remainder.

If a natural number a divides by a natural number b, then it is calculated how many times the number b is contained in a. The result is the quotient q and possibly a remainder r.
We can write: a = b · q + r
Example: 17 : 5 = 3 Rest 2
The remainder is therefore the difference between the dividend and the largest multiple of the divisor

17 - (3 · 5) = 2

A remainder arises only if the dividend is not a multiple of the divisor. In other words, if the dividend is not divisible by the divisor.

## Euclidean division and negative numbers

Dividing numbers with different signs gets the following results:

7 :  3 =  2 remainder  1

-7 :  3 = -2 remainder -1

7 : -3 = -2 remainder  1

-7 : -3 =  2 remainder -1

3 · 2 + 1 = 7

3 · (-2) + (-1) = -7

-3 · (-2) + 1 = 7

-3 · 2 +(-1) = -7

## Arithmetic

Integer and Real Numbers
Complex Numbers
Sets
Roots and Power
Percentage Calculation
Interest Calculation
Absolute Value of a Number
Euclidean division
Modulo - Remainder of a division
Vectors
Matrices