2. \( 4 4 \longdiv { 6 , 6 6 8 } \)

To perform the long division of \( 66,688 \) by \( 44 \), we can follow these steps: 1. **Set up the division**: Write \( 66,688 \) under the long division symbol and \( 44 \) outside. 2. **Divide the first part**: Look at the first two digits of \( 66,688 \), which are \( 66 \). Determine how many times \( 44 \) fits into \( 66 \): - \( 44 \) goes into \( 66 \) once (1 time). - Write \( 1 \) above the division line. 3. **Multiply and subtract**: Multiply \( 1 \) by \( 44 \) to get \( 44 \), and subtract this from \( 66 \): \[ 66 - 44 = 22 \] 4. **Bring down the next digit**: Bring down the next digit from \( 66,688 \), which is \( 6 \), making it \( 226 \). 5. **Divide again**: Determine how many times \( 44 \) fits into \( 226 \): - \( 44 \) goes into \( 226 \) five times (5 times). - Write \( 5 \) above the division line next to \( 1 \). 6. **Multiply and subtract**: Multiply \( 5 \) by \( 44 \) to get \( 220 \), and subtract this from \( 226 \): \[ 226 - 220 = 6 \] 7. **Bring down the next digit**: Bring down the next digit from \( 66,688 \), which is \( 8 \), making it \( 68 \). 8. **Divide again**: Determine how many times \( 44 \) fits into \( 68 \): - \( 44 \) goes into \( 68 \) once (1 time). - Write \( 1 \) above the division line next to \( 15 \). 9. **Multiply and subtract**: Multiply \( 1 \) by \( 44 \) to get \( 44 \), and subtract this from \( 68 \): \[ 68 - 44 = 24 \] 10. **Bring down the next digit**: There are no more digits to bring down, so we can stop here. The remainder is \( 24 \). Putting it all together, we have: \[ 66,688 \div 44 = 1,511 \quad \text{with a remainder of } 24. \] Thus, the final answer is: \[ \boxed{1,511 \text{ R } 24} \]