$ 425 $ with a remainder of 2

$ 612 $ with a remainder of 3

$ 322 $ with a remainder of 1

Long Division Problem: Dividing 1305 by 4 Step-by-Step

Q: What do I do when the first digit is smaller than the divisor?

When 1 is smaller than 4, you combine it with the next digit. So instead of dividing 1 by 4, you divide 13 by 4. This is completely normal in long division!

Q: How do I know how many times 4 goes into each number?

Think of your multiplication tables! For 4 into 13: $ 4 \times 3 = 12 $ (fits), but $ 4 \times 4 = 16 $ (too big). So use 3.

Q: What if I have a remainder at the very end?

That's perfectly normal! In this problem, we get remainder 1 because 1305 doesn't divide evenly by 4. The final answer is 326 remainder 1.

Q: Can I check my answer without doing the whole division again?

Yes! Multiply your quotient by the divisor, then add the remainder: $ 326 \times 4 + 1 = 1304 + 1 = 1305 $ ✓. If you get the original number, you're right!

Q: Why do we subtract after each division step?

Subtracting shows you what's left over after taking out groups of 4. This leftover combines with the next digit to continue the division process.

Long Division with Four-Digit Numbers

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve the problem together.

00:07 Start by dividing the first number on the left.

00:11 One is less than four, so add the next digit. Then divide.

00:17 Write the answer above without the remainder.

00:20 Now multiply the answer by the divisor to continue.

00:24 Subtract the product from your current number.

00:29 Bring down the next digit and repeat the steps.

00:34 It's time to divide again.

00:36 Write the result above, keeping an eye on placement.

00:40 Multiply and subtract once more.

00:45 Bring down the next digit and repeat.

00:48 Divide once again.

00:51 Make sure you write the result in the correct spot.

00:57 Multiply and subtract to keep going.

01:02 We ended up with a remainder of one.

01:07 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve the problem of dividing 1305 by 4, we will use long division.

Step-by-step solution:

Step 1: Divide the first digit of the dividend. 1 (in 1305) is less than 4, so we consider the first two digits, 13.
Step 2: Find how many times 4 goes into 13. It goes 3 times because $4 \times 3 = 12$ .
Step 3: Subtract 12 from 13, leaving a remainder of 1. Bring down the next digit, 0, to make it 10.
Step 4: Determine how many times 4 goes into 10. It goes 2 times because $4 \times 2 = 8$ .
Step 5: Subtract 8 from 10, leaving a remainder of 2. Bring down the next digit, 5, making it 25.
Step 6: See how many times 4 fits into 25. It goes 6 times because $4 \times 6 = 24$ .
Step 7: Subtract 24 from 25, which leaves a remainder of 1.

The quotient from the division is 326, and the remainder is 1.

Therefore, the solution to the division of 1305 by 4 is $326$ with a remainder of 1.

Final Answer

$326$ with a remainder of 1

Key Points to Remember

Essential concepts to master this topic

Foundation: Work left to right, dividing one digit at a time
Technique: When digit is too small, combine with next digit: 1 < 4, so use 13
Check: Multiply quotient by divisor and add remainder: $326 \times 4 + 1 = 1305$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to bring down the next digit
Don't leave a remainder hanging without bringing down the next digit = incomplete division! This stops your work too early and gives a wrong quotient. Always bring down each digit systematically and continue until all digits are used.

Practice Quiz

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FAQ

Everything you need to know about this question

What do I do when the first digit is smaller than the divisor?

When 1 is smaller than 4, you combine it with the next digit. So instead of dividing 1 by 4, you divide 13 by 4. This is completely normal in long division!

How do I know how many times 4 goes into each number?

Think of your multiplication tables! For 4 into 13: $4 \times 3 = 12$ (fits), but $4 \times 4 = 16$ (too big). So use 3.

What if I have a remainder at the very end?

That's perfectly normal! In this problem, we get remainder 1 because 1305 doesn't divide evenly by 4. The final answer is 326 remainder 1.

Can I check my answer without doing the whole division again?

Yes! Multiply your quotient by the divisor, then add the remainder: $326 \times 4 + 1 = 1304 + 1 = 1305$ ✓. If you get the original number, you're right!

Why do we subtract after each division step?

Subtracting shows you what's left over after taking out groups of 4. This leftover combines with the next digit to continue the division process.

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