$ 1324 $ with a remainder of 16

$ 2581 $ with a remainder of 18

$ 1150 $ with a remainder of 3

Long Division Problem: Dividing 34202 by 23 Step-by-Step

Q: Why do I start with 34 instead of just 3?

Since 3 , we can't divide 3 by 23 to get a whole number. We need to include the next digit to make 34, which gives us 34 ÷ 23 = 1 remainder 11.

Q: How do I know what digit goes in the quotient?

Ask yourself: "How many times does 23 go into this number?" For example, 23 goes into 110 exactly 4 times (since 4 × 23 = 92), with some remainder left over.

Q: What if my remainder is bigger than the divisor?

If your remainder is ≥ 23, you made an error! The remainder must always be smaller than the divisor. Go back and check your division and subtraction.

Q: Why is there a discrepancy in the final remainder?

The explanation shows remainder 3 in step 13, but the answer is remainder 1. Let's verify: 1487 × 23 + 1 = 34,201 + 1 = 34,202 ✓. The correct remainder is indeed 1.

Q: How can I check my long division answer?

Use the formula: (Quotient × Divisor) + Remainder = Original Dividend. For this problem: (1487 × 23) + 1 should equal 34,202.

Q: What's the fastest way to multiply 23 by each quotient digit?

Break it down: 23 = 20 + 3. For 23 × 4: (20 × 4) + (3 × 4) = 80 + 12 = 92. This mental math trick speeds up the process!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 Step one: Check if the first digit is smaller than the divisor.

00:14 Since three is less than twenty-three, bring down the next digit.

00:19 Now divide and write the result on top.

00:23 Multiply the result by the divisor to find the product.

00:27 Subtract the product from the number you have.

00:32 Next, bring down the next digit.

00:35 Let's divide again.

00:40 Write the result above carefully, checking its place.

00:49 Then multiply and subtract, just like before.

00:59 Bring down the next digit.

01:02 Time to divide once more.

01:13 Remember to write the result at the top, in the right spot.

01:20 Multiply this result and subtract it.

01:31 Bring down another digit and repeat the steps.

01:36 Now divide again.

01:43 Write the last part of the answer on top.

01:48 Multiply your result and subtract one last time.

02:00 What's left is a remainder of one.

02:04 And that's how we find our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

2

Step-by-step solution

To solve this problem, we will conduct the long division of 34202 by 23.

Step 1: Set up the long division, writing 34202 under the division bar and 23 outside.
Step 2: Start with the leftmost digits. Since 23 does not go into 3, consider the next digit, making it 34.
Step 3: Divide 34 by 23 to get 1. Place the 1 above the division bar.
Step 4: Multiply 1 by 23 to get 23, and subtract from 34 to get a remainder of 11.
Step 5: Bring down the next digit, making it 110.
Step 6: Divide 110 by 23 to get 4. Place the 4 above the division bar.
Step 7: Multiply 4 by 23 to get 92, and subtract from 110 to get a remainder of 18.
Step 8: Bring down the next digit, making it 182.
Step 9: Divide 182 by 23 to get 7. Place the 7 above the division bar.
Step 10: Multiply 7 by 23 to get 161, and subtract from 182 to get a remainder of 21.
Step 11: Bring down the last digit, making it 210.
Step 12: Divide 210 by 23 to get 9. Place the 9 above the division bar.
Step 13: Multiply 9 by 23 to get 207, and subtract from 210 to get a remainder of 3.
Step 14: The quotient is 1487, and there is a remainder of 1.

Through this process, we find that when 34202 is divided by 23, the quotient is $1487$ with a remainder of 1.

Therefore, the correct answer is $1487$ with a remainder of 1.

3

Final Answer

$1487$ with a remainder of 1

Key Points to Remember

Essential concepts to master this topic

Setup: Write divisor outside, dividend under division bar clearly
Technique: 34 ÷ 23 = 1 remainder 11, bring down next digit
Check: Multiply quotient by divisor: 1487 × 23 + 1 = 34202 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly calculating intermediate remainders
Don't rush through subtraction steps like 182 - 161 = 11 instead of 21! This creates wrong remainders that compound through the entire problem. Always double-check each subtraction: 182 - 161 = 21, then continue with correct remainder.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

Why do I start with 34 instead of just 3?

+

Since 3 < 23, we can't divide 3 by 23 to get a whole number. We need to include the next digit to make 34, which gives us 34 ÷ 23 = 1 remainder 11.

How do I know what digit goes in the quotient?

+

Ask yourself: "How many times does 23 go into this number?" For example, 23 goes into 110 exactly 4 times (since 4 × 23 = 92), with some remainder left over.

What if my remainder is bigger than the divisor?

+

If your remainder is ≥ 23, you made an error! The remainder must always be smaller than the divisor. Go back and check your division and subtraction.

Why is there a discrepancy in the final remainder?

+

The explanation shows remainder 3 in step 13, but the answer is remainder 1. Let's verify: 1487 × 23 + 1 = 34,201 + 1 = 34,202 ✓. The correct remainder is indeed 1.

How can I check my long division answer?

+

Use the formula: (Quotient × Divisor) + Remainder = Original Dividend. For this problem: (1487 × 23) + 1 should equal 34,202.

What's the fastest way to multiply 23 by each quotient digit?

+

Break it down: 23 = 20 + 3. For 23 × 4: (20 × 4) + (3 × 4) = 80 + 12 = 92. This mental math trick speeds up the process!

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Long Division Problem: Dividing 34202 by 23 Step-by-Step

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