The division algorithm states that given an integer ${\displaystyle x}$ and a positive integer ${\displaystyle y}$, there are unique integers ${\displaystyle q}$ and ${\displaystyle r}$, with ${\displaystyle 0 \le r < y}$, for which ${\displaystyle x = q y + r}$. For example, when a number is divided by 7, the remainder after division will be an integer between 0 and 6.