Chapter 4, Problem 1RE

Find the quotient and remainder when 11,109,999,999,997 is divided by 1111.

To determine

The quotient and remainder when 11,109,999,999,997 is divided by 1111.

Answer to Problem 1RE

Solution: The quotient is and the remainder is.

Explanation of Solution

We know,

$\begin{array}{l}11,109,999,999,997=11,110,000,000-3\\ =\left(10,000,000\right)\left(1111\right)-3\\ =\left(9,999,999\right)\left(1111\right)+\left(1111-3\right)\\ =\left(9,999,999\right)\left(1111\right)+1008\end{array}$

The quotient is 9,999,999 and the remainder is 1008.