Quotient and remainder of a division

Statement

Use the division algorithm to find the quotient and remainder of the division of $1000$ by $23$.

Solution

We seek $q$ and $r$ with $1000 = 23q + r$ and $0 \le r < 23$. $23 \cdot 43 = 989, \qquad 1000 - 989 = 11.$ Since $0 \le 11 < 23$, the quotient is $\boxed{43}$ and the remainder is $\boxed{11}$: $1000 = 23 \cdot 43 + 11.$