Long Division: Division of a number greater than 3-digits without a remainder

To solve the division $\frac{1250}{2}$, follow these steps:

• Step 1: Start with the first digit of 1250, which is 1. 2 does not fit into 1, so consider the first two digits, 12.
• Step 2: Divide 12 by 2: $12 \div 2 = 6$. Place 6 in the quotient. Multiply 6 by 2 to get 12, and subtract this from 12, resulting in 0.
• Step 3: Bring down the next digit, which is 5. Now, divide 5 by 2: $5 \div 2 = 2$ (since 2 goes into 5 two times). Multiply 2 by 2 to get 4, subtract from 5, leaving 1.
• Step 4: Bring down the final digit, 0. Divide 10 by 2: $10 \div 2 = 5$. Multiply 5 by 2 to get 10, leaving a remainder of 0.

So, the quotient of $\frac{1250}{2}$ is $625$.

Therefore, the solution to the problem is $625$.

To solve the division $3412 \div 2$, we will use long division:

• Step 1: Start with the leftmost digit. Divide 3 by 2, which goes 1 time. Write 1 above the division bar. Multiply 1 by 2, subtract from 3 to get a remainder of 1.
• Step 2: Bring down the next digit (4) to get 14. Divide 14 by 2, which is 7. Write 7 above the division bar. Multiply 7 by 2, subtract from 14 to get 0.
• Step 3: Bring down the next digit (1) to get 1. Divide 1 by 2, which goes 0 times. Write 0 above the division bar.
• Step 4: Bring down the final digit (2) to get 12. Divide 12 by 2, which is 6. Write 6 above the division bar. Multiply 6 by 2, which equals 12. Subtract from 12 to get 0.
• Since all digits have been brought down and divided with a remainder of 0, the quotient is the complete result of the division.

Therefore, the final quotient is $\mathbf{1706}$.

To solve this problem, we'll follow the steps of long division to divide 9120 by 3:

Step 1: Divide the thousands place:
- 3 goes into 9 three times. Multiply 3 by 3 to get 9. Subtract 9 from 9 to get 0.

Step 2: Bring down the next digit (1):
- 3 goes into 1 zero times. Multiply 3 by 0 to get 0. Subtract 0 from 1 to keep 1.

Step 3: Bring down the next digit (2):
- Now divide 12 by 3, which equals 4. Multiply 3 by 4 to get 12. Subtract 12 from 12 to get 0.

Step 4: Finally, bring down the last digit (0):
- 3 goes into 0 zero times. Thus, the result of this step is 0.

Therefore, the quotient when 9120 is divided by 3 is $3040$.

To solve this division problem, we will use the long division method to divide 1040 by 4.

Step 1: Set up the division.
The dividend is 1040, and the divisor is 4. We will determine how many times 4 can fit into each part of 1040.

Step 2: Division of each digit group.
- Divide the first digit: 10 (from 1040) by 4. The result is 2, since 4 fits into 10 two times (4x2=8).
- Subtract 8 from 10, leaving a remainder of 2. Bring down the next digit 4 to make it 24.
- Divide 24 by 4. The result is 6, since 4 fits into 24 six times (4x6=24).
- Subtract 24 from 24, leaving no remainder.
- Bring down the last digit: 0. 0 divided by 4 is 0.

Step 3: Combine the results.
The results of our divisions are combined to form the complete quotient of 260.

Therefore, when 1040 is divided by 4, the quotient is $260$.

To solve the division problem $1250 \div 5$, we will use long division.

• Step 1: Identify the first part of the dividend (1250) that is divisible by 5. We start with the first digit, which is 1. Since 1 is less than 5, we consider the first two digits, 12.
• Step 2: Determine how many times 5 fits into 12. It fits 2 times since $5 \times 2 = 10$. Write 2 above the long division bar.
• Step 3: Subtract 10 from 12, leaving a remainder of 2. Bring down the next digit, 5, making it 25.
• Step 4: Determine how many times 5 goes into 25. It fits exactly 5 times since $5 \times 5 = 25$. Write 5 above the bar, next to 2.
• Step 5: Subtract 25 from 25, leaving a remainder of 0. Bring down the last digit, 0, making it 00.
• Step 6: Since 5 goes into 0 exactly 0 times, write 0 above the division bar as the last digit of the quotient.

After completing the division, the result above the division bar shows the quotient: $250$.

Therefore, the solution to the problem is $250$.

To solve this problem, we'll use the long division method to divide $7714$ by $7$:

1. Consider the first digit of the dividend, $7$. How many times does $7$ go into $7$? It fits 1 time.

2. Write $1$ in the quotient and subtract $7 \times 1 = 7$ from the digit to get $0$. Next, bring down the next digit, which is $7$, making the number $07$.

3. Determine how many times $7$ fits into $07$. It fits no times, so write $0$ in the quotient, resulting in $10$ in the quotient so far. Bring down the next digit $1$, making it $71$.

4. How many times does $7$ go into $71$? It fits 10 times. Write a $1$ in the quotient next to the existing one, making $110$.

5. Subtract $7 \times 10 = 70$, resulting in $1$. Bring down the next digit $4$, making it $14$.

6. How many times does $7$ go into $14$? It fits 2 times. Write $2$ in the quotient, yielding a final quotient of $1102$.

Subtract $7 \times 2 = 14$ from $14$, resulting in a remainder of $0$, indicating division is complete with no remainder.

Therefore, the quotient when $7714$ is divided by $7$ is $1102$.

To solve this problem, we'll perform long division of 8160 by 8:

• Step 1: Begin with the first digit. Divide 8 (the divisor) into 8 (the first digit of 8160), which goes 1 time. Thus, the first digit of the quotient is 1.
• Step 2: Multiply 8 (divisor) by 1 (quotient part) to get 8. Subtract 8 from 8 to get 0. Bring down the next digit, which is 1.
• Step 3: Divide 8 into 1. Since it doesn't go fully, note 0 in the quotient and bring down the next digit, 6, making it 16.
• Step 4: Now divide 8 into 16, which goes 2 times. So, write 2 in the quotient.
• Step 5: Multiply 8 by 2 to get 16, subtract to get 0, and bring down the final digit, 0.
• Step 6: Divide 8 into 0, which is 0, and that's the final digit of the quotient.

Therefore, the quotient of dividing 8160 by 8 is $\mathbf{1020}$.

To solve the problem of dividing $15003$ by $3$, we will use the long division method. Let's break it down step-by-step:

• Step 1: Begin with the first digit of $15003$, which is $1$. Since $1$ divided by $3$ is $0$, we can't use this, so we consider the first two digits, which are $15$.
• Step 2: Divide $15$ by $3$. The result is $5$ because $5 \times 3 = 15$. Subtract $15$ from $15$ to get $0$.
• Step 3: Bring down the next digit, which is $0$. Now, we have $0$ to divide by $3$, which results in $0$. Write $0$ next to $5$ in the quotient.
• Step 4: Bring down the next digit, which is again $0$. Divide $0$ by $3$ to get $0$. Write $0$ in the quotient, making it $500$.
• Step 5: Finally, bring down the last digit, which is $3$. Divide $3$ by $3$ to get $1$. Write $1$ in the quotient, making it $5001$.

The division is complete as there are no more digits to bring down. Hence, the quotient of dividing $15003$ by $3$ is:

$5001$.

To solve this problem, we will perform long division of the number 42513 by 3 step by step:

• Step 1: Look at the first digit of 42513, which is 4. Divide 4 by 3, which gives 1. Write 1 as the first digit of the quotient.
• Step 2: Multiply 1 by 3 (the divisor) to get 3. Subtract 3 from 4, leaving 1.
• Step 3: Bring down the next digit, 2, making the new number 12.
• Step 4: Divide 12 by 3, which equals 4. Write 4 as the next digit in the quotient.
• Step 5: Multiply 4 by 3 to get 12 and subtract from 12, leaving 0.
• Step 6: Bring down the next digit, 5, making the new number 5.
• Step 7: Divide 5 by 3, which gives 1. Write 1 in the quotient.
• Step 8: Multiply 1 by 3 to get 3 and subtract from 5, leaving 2.
• Step 9: Bring down the next digit, 1, making the new number 21.
• Step 10: Divide 21 by 3, which equals 7. Write 7 in the quotient.
• Step 11: Multiply 7 by 3 to get 21 and subtract from 21, leaving 0.
• Step 12: Bring down the final digit, 3.
• Step 13: Divide 3 by 3, which equals 1. Write 1 in the quotient.
• Step 14: Multiply 1 by 3 to get 3 and subtract from 3, leaving 0.

Thus, the division is complete, and there is no remainder. The quotient of 42513 divided by 3 is $14171$.

Therefore, the solution to the problem is $14171$.

To solve the problem of dividing $20004$ by $4$ using long division, follow these steps:

• Step 1: Start with the leftmost digit of the dividend. Divide the digit $2$ by $4$. Since $2$ is less than $4$, the result for this step is $0$, and we carry the number $2$ to the next digit.
• Step 2: Combine the next digit $0$ with the carry-over, making it $20$. Divide $20$ by $4$ to get $5$. Write $5$ in the quotient.
• Step 3: Move to the next digit of the dividend, which is another $0$. Bring down this $0$ next to the remainder of the previous division to make it $00$. Divide $0$ by $4$ to get $0$ and write this in the quotient.
• Step 4: Consider the next digit of the dividend: $0$ again, bringing down to again divide by $4$. This yields another $0$ in the quotient.
• Step 5: Finally, move to the last digit of the dividend, $4$. Combine it with the current result $00$ to get $04$. Divide $4$ by $4$ to obtain $1$, which is added to the quotient.

After performing these divisions, the complete quotient is $5001$.

Therefore, the solution to the problem of dividing $20004$ by $4$ is $5001$.

Let's solve the division of 32412 by 6 using long division step-by-step:

• Step 1: Start with the leftmost digit of the dividend, which is 3. Divide 3 by 6; it's less than 6, so we consider the first two digits, 32.
• Step 2: Divide 32 by 6. The largest number less than or equal to 32 that 6 can multiply to is 30 (6 x 5). The quotient here is 5.
• Step 3: Subtract 30 from 32, leaving a remainder of 2. Bring down the next digit, 4, making the new number 24.
• Step 4: Divide 24 by 6. 6 goes into 24 exactly 4 times. Write 4 in the quotient.
• Step 5: Subtract 24 from 24, leaving 0. Bring down the next digit, 1.
• Step 6: Divide 1 by 6; it's less than 6, so write 0 next to the quotient. Bring down the next digit, 2, making it 12.
• Step 7: Divide 12 by 6. 6 goes into 12 exactly 2 times. Write 2 in the quotient.
• Step 8: Subtract 12 from 12, leaving 0, and as there are no more digits to bring down, the division is complete.

Therefore, the final quotient of the division $32412 \div 6$ is $5402$.

To solve this problem, we'll employ the long division method:

• Step 1: Divide the first part of the number that is greater than or equal to the divisor. Start with 20 (from 20416).
• Step 2: $20 \div 8 = 2$. Write 2 as the part of the quotient. Multiply: $2 \times 8 = 16$. Subtract $16$ from $20$ to get $4$.
• Step 3: Bring down the next digit from the dividend (20416), making it $44$.
• Step 4: $44 \div 8 = 5$. Write 5 to the quotient. Multiply: $5 \times 8 = 40$. Subtract $40$ from $44$ to get $4$.
• Step 5: Bring down the next digit, making it $41$.
• Step 6: $41 \div 8 = 5$. Write 5 to the quotient. Multiply: $5 \times 8 = 40$. Subtract $40$ from $41$ to get $1$.
• Step 7: Bring down the next digit, making it $16$.
• Step 8: $16 \div 8 = 2$. Write 2 to the quotient. Multiply: $2 \times 8 = 16$. Subtract $16$ from $16$ to get $0$.

The complete quotient of $20416 \div 8$ is $2552$, with no remainder. Therefore, the selected answer is the correct one.

The solution to the division is $2552$.