$ 3216 $ with a remainder of 2

$ 5216 $ with a remainder of 12

$ 2836 $ with a remainder of 1

Long Division Problem: Dividing 52103 by 29 Step-by-Step

Q: What if 29 doesn't go into the first digits evenly?

That's normal! Start with 52 ÷ 29 = 1 with remainder 23. The remainder becomes part of your next step when you bring down the next digit.

Q: How do I know if 29 goes into 231 seven times or eight times?

Use multiplication: $ 29 \times 7 = 203 $ and $ 29 \times 8 = 232 $. Since 232 > 231, use 7 times!

Q: Why is there still a remainder at the end?

When the final remainder (19) is smaller than the divisor (29), you stop dividing. The remainder 19 means 52103 = 29 × 1796 + 19.

Q: What if I make an error in the middle steps?

Don't panic! Long division errors usually show up when your remainder becomes larger than the divisor. Go back and check your most recent multiplication and subtraction.

Long Division with Large Dividends

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's start by dividing the leftmost digit in the dividend

00:08 5 is less than 29, so we'll add the next digit and then divide

00:17 Write the result without remainder above, pay attention to the position

00:22 Now multiply the result by the divisor

00:25 Subtract the product from the number

00:30 Now bring down the next digit below and use the same steps

00:34 Divide

00:39 Write the result without remainder above, pay attention to the position

00:43 Multiply the result and subtract

00:53 Now bring down the next digit below and use the same steps

00:59 Divide

01:04 Write the result without remainder above, pay attention to the position

01:10 Multiply the result and subtract

01:17 Now bring down the next digit below and use the same steps

01:20 Divide

01:24 Write the result without remainder above, pay attention to the position

01:33 Multiply the result and subtract

01:42 We got a remainder of 19

01:46 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve this problem, we will perform a long division of 52103 by 29 and determine both the quotient and the remainder.

Let's divide 52103 by 29 using long division:

First, see how many times 29 can go into the first few digits of 52103, starting from the left.
29 into 52 goes 1 time. Multiply $29 \times 1 = 29$ . Subtract 29 from 52, giving us 23.
Bring down the next digit forming 231.
29 into 231 goes 7 times. Multiply $29 \times 7 = 203$ . Subtract 203 from 231, giving us 28.
Bring down the next digit forming 280.
29 into 280 goes 9 times. Multiply $29 \times 9 = 261$ . Subtract 261 from 280, giving us 19.
Bring down the last digit forming 193.
29 into 193 goes 6 times. Multiply $29 \times 6 = 174$ . Subtract 174 from 193, giving us 19.

The quotient of the division of 52103 by 29 is 1796 with a remainder of 19, which matches choice 4.

Therefore, the correct answer is: $1796$ with a remainder of 19.

Final Answer

$1796$ with a remainder of 19

Key Points to Remember

Essential concepts to master this topic

Process: Divide, multiply, subtract, bring down next digit, repeat
Technique: Start with 29 into 52 = 1 remainder 23
Check: Verify $1796 \times 29 + 19 = 52103$ ✓

Common Mistakes

Avoid these frequent errors

Estimating how many times divisor goes into partial dividend
Don't guess wildly how many times 29 goes into 231 = wrong quotient digits! Poor estimation leads to excessive corrections and confusion. Always use multiplication facts: try 7 since 29 × 7 = 203 is close to 231.

Practice Quiz

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FAQ

Everything you need to know about this question

What if 29 doesn't go into the first digits evenly?

That's normal! Start with 52 ÷ 29 = 1 with remainder 23. The remainder becomes part of your next step when you bring down the next digit.

How do I know if 29 goes into 231 seven times or eight times?

Use multiplication: $29 \times 7 = 203$ and $29 \times 8 = 232$ . Since 232 > 231, use 7 times!

Why is there still a remainder at the end?

When the final remainder (19) is smaller than the divisor (29), you stop dividing. The remainder 19 means 52103 = 29 × 1796 + 19.

How can I check my long division answer?

Multiply your quotient by the divisor, then add the remainder: $1796 \times 29 + 19$ . If you get the original dividend (52103), you're correct!

What if I make an error in the middle steps?

Don't panic! Long division errors usually show up when your remainder becomes larger than the divisor. Go back and check your most recent multiplication and subtraction.

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