how do you divide with a remainder

A division algorithm is often discussed in introductions to abstract

algebra or number theory. The intent is to explain ordinary division

of integers in a more theoretical light that allows certain

generalizations to things such as polynomials and other subsets

ot the real or complex numbers.

Given positive integers n and m, the division of n by m, n/m,

is to find whole numbers q and r so that

n = m * q + r, or n/m = q + r/m

with 0 <= r < m.

The integer q is called the quotient and r is called the remainder.

In this case little is required, since

2 = 86 * 0 + 2

so that the quotient is 0 and the remainder is 2.

## Comments

2/86 is also 1/43 when reduced to lowest terms.