To solve the division of [tex]\( 671 \)[/tex] by [tex]\( 3 \)[/tex], we will go through the long division process step-by-step:
1. Divide the first digit of the dividend by the divisor:
- The first digit of [tex]\( 671 \)[/tex] is [tex]\( 6 \)[/tex].
- Divide [tex]\( 6 \)[/tex] by [tex]\( 3 \)[/tex], which goes [tex]\( 2 \)[/tex] times (since [tex]\( 3 \times 2 = 6 \)[/tex]).
- Place the [tex]\( 2 \)[/tex] above the division bar.
2. Multiply and subtract:
- Multiply [tex]\( 2 \)[/tex] by [tex]\( 3 \)[/tex] to get [tex]\( 6 \)[/tex].
- Subtract [tex]\( 6 \)[/tex] from [tex]\( 6 \)[/tex] to get [tex]\( 0 \)[/tex].
- Write [tex]\( 0 \)[/tex] below the [tex]\( 6 \)[/tex].
3. Bring down the next digit:
- The next digit in the dividend is [tex]\( 7 \)[/tex].
- Bring down the [tex]\( 7 \)[/tex] next to the [tex]\( 0 \)[/tex] to form [tex]\( 07 \)[/tex].
4. Divide the new number by the divisor:
- Now divide [tex]\( 7 \)[/tex] by [tex]\( 3 \)[/tex], which goes [tex]\( 2 \)[/tex] times (since [tex]\( 3 \times 2 = 6 \)[/tex]).
- Place the [tex]\( 2 \)[/tex] above the division bar, next to the first [tex]\( 2 \)[/tex].
5. Multiply and subtract:
- Multiply [tex]\( 2 \)[/tex] by [tex]\( 3 \)[/tex] to get [tex]\( 6 \)[/tex].
- Subtract [tex]\( 6 \)[/tex] from [tex]\( 7 \)[/tex] to get [tex]\( 1 \)[/tex].
- Write [tex]\( 1 \)[/tex] below the [tex]\( 7 \)[/tex].
6. Bring down the next digit:
- The next digit in the dividend is [tex]\( 1 \)[/tex].
- Bring down the [tex]\( 1 \)[/tex] next to the [tex]\( 1 \)[/tex] to form [tex]\( 11 \)[/tex].
7. Divide the new number by the divisor:
- Now divide [tex]\( 11 \)[/tex] by [tex]\( 3 \)[/tex], which goes [tex]\( 3 \)[/tex] times (since [tex]\( 3 \times 3 = 9 \)[/tex]).
- Place the [tex]\( 3 \)[/tex] above the division bar, next to the second [tex]\( 2 \)[/tex].
8. Multiply and subtract:
- Multiply [tex]\( 3 \)[/tex] by [tex]\( 3 \)[/tex] to get [tex]\( 9 \)[/tex].
- Subtract [tex]\( 9 \)[/tex] from [tex]\( 11 \)[/tex] to get [tex]\( 2 \)[/tex].
- Write [tex]\( 2 \)[/tex] below the [tex]\( 11 \)[/tex].
Since there are no more digits left to bring down, we have completed the division.
The quotient is [tex]\( 223 \)[/tex] and the remainder is [tex]\( 2 \)[/tex].
Therefore, [tex]\(\frac{671}{3} = 223 \, R2\)[/tex].
