To perform the division of 2758 by 7 and find the quotient and remainder, follow these steps:
### Step-by-Step Solution
1. Divide the first digit:
- The first digit of the dividend (2758) is 2.
- 2 divided by 7 is 0 because 2 is less than 7.
- Write down 0, and bring down the next digit (7) making it 27.
2. Divide 27 by 7:
- 27 divided by 7 is 3 because [tex]\(7 \times 3 = 21\)[/tex] and that's the largest multiple of 7 that is less than 27.
- Write down 3.
- Subtract [tex]\(21\)[/tex] from [tex]\(27\)[/tex] to get a remainder of [tex]\(6\)[/tex].
- Bring down the next digit (5), making it 65.
3. Divide 65 by 7:
- 65 divided by 7 is 9 because [tex]\(7 \times 9 = 63\)[/tex] and that's the largest multiple of 7 that fits into 65.
- Write down 9.
- Subtract [tex]\(63\)[/tex] from [tex]\(65\)[/tex] to get a remainder of [tex]\(2\)[/tex].
- Bring down the next digit (8), making it 28.
4. Divide 28 by 7:
- 28 divided by 7 is 4 because [tex]\(7 \times 4 = 28\)[/tex].
- Write down 4.
- Subtract [tex]\(28\)[/tex] from [tex]\(28\)[/tex] to get a remainder of [tex]\(0\)[/tex].
Since there are no more digits to bring down, the final result of the division is a quotient of 394 and a remainder of 0.
Thus,
[tex]\[ 7 \longdiv { 2 , 7 5 8 } = 394 \text{ remainder } 0 \][/tex]
