Euclidean division is the process of dividing one integer by another, in a way that produces an integer quotient and an integer remainder.

Division Theorem

Euclidean division is based on the following result:

Given two integers and where , there exist integers (quotient) and (remainder) such that

and

Quotient

The quotient in euclidean division describes the maximum number of times the divisor can be subtracted from the dividend without the result becoming negative.

Remainder

The quotient in euclidean division describes the leftover after the quotient the divisor is subtracted from the dividend.

The remainder can of a euclidean division can be given by the following equation:

Examples

What is the Quotient when Dividing 7 by 2

2 can go into 7 evenly 3 times so the quotient is 3, and the remainder is 1

What is the Quotient when Dividing 4 by 2

2 can go into 4 evenly 2 times so the quotient is 2, and the remainder is 0