6-Digit by 2-Digit Long Division with Remainders and Steps Shown ... - Free Printable

The task involves performing long division for each of the given problems. Let's solve each problem step by step.

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Problem 1: \( 68 \div 662425 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 662425 \) by \( 68 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 66 \). Since \( 66 < 68 \), consider the first three digits, \( 662 \).
- Determine how many times \( 68 \) goes into \( 662 \):
\[
662 \div 68 \approx 9 \quad (\text{since } 68 \times 9 = 612)
\]
3. Multiply and subtract:
- Multiply \( 68 \times 9 = 612 \).
- Subtract: \( 662 - 612 = 50 \).
4. Bring down the next digit:
- Bring down the next digit, \( 4 \), to make it \( 504 \).
5. Repeat the process:
- Determine how many times \( 68 \) goes into \( 504 \):
\[
504 \div 68 \approx 7 \quad (\text{since } 68 \times 7 = 476)
\]
- Multiply \( 68 \times 7 = 476 \).
- Subtract: \( 504 - 476 = 28 \).
6. Bring down the next digit:
- Bring down the next digit, \( 2 \), to make it \( 282 \).
7. Repeat the process:
- Determine how many times \( 68 \) goes into \( 282 \):
\[
282 \div 68 \approx 4 \quad (\text{since } 68 \times 4 = 272)
\]
- Multiply \( 68 \times 4 = 272 \).
- Subtract: \( 282 - 272 = 10 \).
8. Bring down the next digit:
- Bring down the next digit, \( 5 \), to make it \( 105 \).
9. Repeat the process:
- Determine how many times \( 68 \) goes into \( 105 \):
\[
105 \div 68 \approx 1 \quad (\text{since } 68 \times 1 = 68)
\]
- Multiply \( 68 \times 1 = 68 \).
- Subtract: \( 105 - 68 = 37 \).

The quotient is \( 9741 \) with a remainder of \( 37 \).

Final Answer for Problem 1:
\[
\boxed{9741}
\]

---

Problem 2: \( 14 \div 824281 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 824281 \) by \( 14 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 82 \). Determine how many times \( 14 \) goes into \( 82 \):
\[
82 \div 14 \approx 5 \quad (\text{since } 14 \times 5 = 70)
\]
3. Multiply and subtract:
- Multiply \( 14 \times 5 = 70 \).
- Subtract: \( 82 - 70 = 12 \).
4. Bring down the next digit:
- Bring down the next digit, \( 4 \), to make it \( 124 \).
5. Repeat the process:
- Determine how many times \( 14 \) goes into \( 124 \):
\[
124 \div 14 \approx 8 \quad (\text{since } 14 \times 8 = 112)
\]
- Multiply \( 14 \times 8 = 112 \).
- Subtract: \( 124 - 112 = 12 \).
6. Bring down the next digit:
- Bring down the next digit, \( 2 \), to make it \( 122 \).
7. Repeat the process:
- Determine how many times \( 14 \) goes into \( 122 \):
\[
122 \div 14 \approx 8 \quad (\text{since } 14 \times 8 = 112)
\]
- Multiply \( 14 \times 8 = 112 \).
- Subtract: \( 122 - 112 = 10 \).
8. Bring down the next digit:
- Bring down the next digit, \( 8 \), to make it \( 108 \).
9. Repeat the process:
- Determine how many times \( 14 \) goes into \( 108 \):
\[
108 \div 14 \approx 7 \quad (\text{since } 14 \times 7 = 98)
\]
- Multiply \( 14 \times 7 = 98 \).
- Subtract: \( 108 - 98 = 10 \).
10. Bring down the next digit:
- Bring down the next digit, \( 1 \), to make it \( 101 \).
11. Repeat the process:
- Determine how many times \( 14 \) goes into \( 101 \):
\[
101 \div 14 \approx 7 \quad (\text{since } 14 \times 7 = 98)
\]
- Multiply \( 14 \times 7 = 98 \).
- Subtract: \( 101 - 98 = 3 \).

The quotient is \( 58879 \) with a remainder of \( 3 \).

Final Answer for Problem 2:
\[
\boxed{58879}
\]

---

Problem 3: \( 14 \div 245582 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 245582 \) by \( 14 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 24 \). Determine how many times \( 14 \) goes into \( 24 \):
\[
24 \div 14 \approx 1 \quad (\text{since } 14 \times 1 = 14)
\]
3. Multiply and subtract:
- Multiply \( 14 \times 1 = 14 \).
- Subtract: \( 24 - 14 = 10 \).
4. Bring down the next digit:
- Bring down the next digit, \( 5 \), to make it \( 105 \).
5. Repeat the process:
- Determine how many times \( 14 \) goes into \( 105 \):
\[
105 \div 14 \approx 7 \quad (\text{since } 14 \times 7 = 98)
\]
- Multiply \( 14 \times 7 = 98 \).
- Subtract: \( 105 - 98 = 7 \).
6. Bring down the next digit:
- Bring down the next digit, \( 5 \), to make it \( 75 \).
7. Repeat the process:
- Determine how many times \( 14 \) goes into \( 75 \):
\[
75 \div 14 \approx 5 \quad (\text{since } 14 \times 5 = 70)
\]
- Multiply \( 14 \times 5 = 70 \).
- Subtract: \( 75 - 70 = 5 \).
8. Bring down the next digit:
- Bring down the next digit, \( 8 \), to make it \( 58 \).
9. Repeat the process:
- Determine how many times \( 14 \) goes into \( 58 \):
\[
58 \div 14 \approx 4 \quad (\text{since } 14 \times 4 = 56)
\]
- Multiply \( 14 \times 4 = 56 \).
- Subtract: \( 58 - 56 = 2 \).
10. Bring down the next digit:
- Bring down the next digit, \( 2 \), to make it \( 22 \).
11. Repeat the process:
- Determine how many times \( 14 \) goes into \( 22 \):
\[
22 \div 14 \approx 1 \quad (\text{since } 14 \times 1 = 14)
\]
- Multiply \( 14 \times 1 = 14 \).
- Subtract: \( 22 - 14 = 8 \).

The quotient is \( 17544 \) with a remainder of \( 8 \).

Final Answer for Problem 3:
\[
\boxed{17544}
\]

---

Problem 4: \( 52 \div 753612 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 753612 \) by \( 52 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 75 \). Determine how many times \( 52 \) goes into \( 75 \):
\[
75 \div 52 \approx 1 \quad (\text{since } 52 \times 1 = 52)
\]
3. Multiply and subtract:
- Multiply \( 52 \times 1 = 52 \).
- Subtract: \( 75 - 52 = 23 \).
4. Bring down the next digit:
- Bring down the next digit, \( 3 \), to make it \( 233 \).
5. Repeat the process:
- Determine how many times \( 52 \) goes into \( 233 \):
\[
233 \div 52 \approx 4 \quad (\text{since } 52 \times 4 = 208)
\]
- Multiply \( 52 \times 4 = 208 \).
- Subtract: \( 233 - 208 = 25 \).
6. Bring down the next digit:
- Bring down the next digit, \( 6 \), to make it \( 256 \).
7. Repeat the process:
- Determine how many times \( 52 \) goes into \( 256 \):
\[
256 \div 52 \approx 4 \quad (\text{since } 52 \times 4 = 208)
\]
- Multiply \( 52 \times 4 = 208 \).
- Subtract: \( 256 - 208 = 48 \).
8. Bring down the next digit:
- Bring down the next digit, \( 1 \), to make it \( 481 \).
9. Repeat the process:
- Determine how many times \( 52 \) goes into \( 481 \):
\[
481 \div 52 \approx 9 \quad (\text{since } 52 \times 9 = 468)
\]
- Multiply \( 52 \times 9 = 468 \).
- Subtract: \( 481 - 468 = 13 \).
10. Bring down the next digit:
- Bring down the next digit, \( 2 \), to make it \( 132 \).
11. Repeat the process:
- Determine how many times \( 52 \) goes into \( 132 \):
\[
132 \div 52 \approx 2 \quad (\text{since } 52 \times 2 = 104)
\]
- Multiply \( 52 \times 2 = 104 \).
- Subtract: \( 132 - 104 = 28 \).

The quotient is \( 14492 \) with a remainder of \( 28 \).

Final Answer for Problem 4:
\[
\boxed{14492}
\]

---

Problem 5: \( 23 \div 748815 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 748815 \) by \( 23 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 74 \). Determine how many times \( 23 \) goes into \( 74 \):
\[
74 \div 23 \approx 3 \quad (\text{since } 23 \times 3 = 69)
\]
3. Multiply and subtract:
- Multiply \( 23 \times 3 = 69 \).
- Subtract: \( 74 - 69 = 5 \).
4. Bring down the next digit:
- Bring down the next digit, \( 8 \), to make it \( 58 \).
5. Repeat the process:
- Determine how many times \( 23 \) goes into \( 58 \):
\[
58 \div 23 \approx 2 \quad (\text{since } 23 \times 2 = 46)
\]
- Multiply \( 23 \times 2 = 46 \).
- Subtract: \( 58 - 46 = 12 \).
6. Bring down the next digit:
- Bring down the next digit, \( 8 \), to make it \( 128 \).
7. Repeat the process:
- Determine how many times \( 23 \) goes into \( 128 \):
\[
128 \div 23 \approx 5 \quad (\text{since } 23 \times 5 = 115)
\]
- Multiply \( 23 \times 5 = 115 \).
- Subtract: \( 128 - 115 = 13 \).
8. Bring down the next digit:
- Bring down the next digit, \( 1 \), to make it \( 131 \).
9. Repeat the process:
- Determine how many times \( 23 \) goes into \( 131 \):
\[
131 \div 23 \approx 5 \quad (\text{since } 23 \times 5 = 115)
\]
- Multiply \( 23 \times 5 = 115 \).
- Subtract: \( 131 - 115 = 16 \).
10. Bring down the next digit:
- Bring down the next digit, \( 5 \), to make it \( 165 \).
11. Repeat the process:
- Determine how many times \( 23 \) goes into \( 165 \):
\[
165 \div 23 \approx 7 \quad (\text{since } 23 \times 7 = 161)
\]
- Multiply \( 23 \times 7 = 161 \).
- Subtract: \( 165 - 161 = 4 \).

The quotient is \( 32557 \) with a remainder of \( 4 \).

Final Answer for Problem 5:
\[
\boxed{32557}
\]

---

Problem 6: \( 64 \div 850826 \)

#### Step-by-Step Solution:
1. Set up the division: Divide \( 850826 \) by \( 64 \).
2. Estimate the first digit:
- Look at the first two digits of the dividend, \( 85 \). Determine how many times \( 64 \) goes into \( 85 \):
\[
85 \div 64 \approx 1 \quad (\text{since } 64 \times 1 = 64)
\]
3. Multiply and subtract:
- Multiply \( 64 \times 1 = 64 \).
- Subtract: \( 85 - 64 = 21 \).
4. Bring down the next digit:
- Bring down the next digit, \( 0 \), to make it \( 210 \).
5. Repeat the process:
- Determine how many times \( 64 \) goes into \( 210 \):
\[
210 \div 64 \approx 3 \quad (\text{since } 64 \times 3 = 192)
\]
- Multiply \( 64 \times 3 = 192 \).
- Subtract: \( 210 - 192 = 18 \).
6. Bring down the next digit:
- Bring down the next digit, \( 8 \), to make it \( 188 \).
7. Repeat the process:
- Determine how many times \( 64 \) goes into \( 188 \):
\[
188 \div 64 \approx 2 \quad (\text{since } 64 \times 2 = 128)
\]
- Multiply \( 64 \times 2 = 128 \).
- Subtract: \( 188 - 128 = 60 \).
8. Bring down the next digit:
- Bring down the next digit, \( 2 \), to make it \( 602 \).
9. Repeat the process:
- Determine how many times \( 64 \) goes into \( 602 \):
\[
602 \div 64 \approx 9 \quad (\text{since } 64 \times 9 = 576)
\]
- Multiply \( 64 \times 9 = 576 \).
- Subtract: \( 602 - 576 = 26 \).
10. Bring down the next digit:
- Bring down the next digit, \( 6 \), to make it \( 266 \).
11. Repeat the process:
- Determine how many times \( 64 \) goes into \( 266 \):
\[
266 \div 64 \approx 4 \quad (\text{since } 64 \times 4 = 256)
\]
- Multiply \( 64 \times 4 = 256 \).
- Subtract: \( 266 - 256 = 10 \).

The quotient is \( 13325 \) with a remainder of \( 10 \).

Final Answer for Problem 6:
\[
\boxed{13325}
\]

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Final Answers for All Problems:

\[
\boxed{9741, 58879, 17544, 14492, 32557, 13325}
\]