The division algorithm
When we try to divide an integer a (the dividend) by a positive integer
d (the divisor), we get an integer q, called the quotient, and an integer
r with 0 ? r < d, called the remainder, such that a = dq + r.
A theorem called “The Division Algorithm” (which, however, is not an
“algorithm” at all) states that the quotient and the remainder are unique.
Examples. What are the quotient and the remainder: