Solve Long Division: 252 ÷ 7 Step by Step

Q: How do I know which number to multiply by the divisor?

Ask yourself: "What's the largest number I can multiply by 7 that doesn't go over 25?" Since 3 × 7 = 21 and 4 × 7 = 28, the answer is 3.

Q: What does 'bring down' mean in long division?

After subtracting, you bring down the next digit from the dividend to continue dividing. It's like moving the digit down to join your remainder.

Q: How do I check if my long division answer is correct?

Multiply your answer by the divisor: $ 36 \times 7 = 252 $. If you get the original dividend back, your answer is correct!

Long Division with Three-Digit 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

00:07 7 is greater than 2, so we'll bring down the next digit and then divide

00:12 Write the result without remainder above, pay attention to the position

00:16 Now multiply the result by the divisor

00:20 Subtract the product from the number

00:26 Now bring down the next digit below and use the same steps

00:32 Divide

00:37 Write the result above

00:40 Multiply the result, subtract

00:48 We got a remainder of 0

00:52 And this is the solution to the problem

Step-by-step written solution

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Understand the problem

Step-by-step solution

To solve this problem, we'll utilize the long division method to divide 252 by 7:

Start by dividing the first digit (2) of 252 by 7. Since 2 is less than 7, consider the first two digits (25).
Divide 25 by 7. The largest integer quotient is 3 because $3 \times 7 = 21$ . Write 3 above the division bar.
Subtract 21 from 25 to get a remainder of 4.
Bring down the next digit (2) to make the new number 42.
Divide 42 by 7. The quotient is 6 because $6 \times 7 = 42$ .
Subtract 42 from 42, resulting in a remainder of 0.

Since there are no more digits to bring down and the remainder is 0, the division is complete.

The quotient of 252 divided by 7 is $36$ .

Comparing this result with the given choices, we see that choice 3 is correct.

Final Answer

$36$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide left to right, using largest possible quotient digits
Technique: 25 ÷ 7 = 3 remainder 4, then bring down 2
Check: Multiply back: 36 × 7 = 252 ✓

Common Mistakes

Avoid these frequent errors

Trying to divide single digits that are smaller than divisor
Don't try to divide 2 ÷ 7 alone = impossible division! Single digits less than the divisor can't be divided. Always combine digits until you have a number larger than your divisor before attempting division.

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 the first digit (like 2) is smaller than the divisor (7), you combine it with the next digit. So instead of trying 2 ÷ 7, you work with 25 ÷ 7.

How do I know which number to multiply by the divisor?

Ask yourself: "What's the largest number I can multiply by 7 that doesn't go over 25?" Since 3 × 7 = 21 and 4 × 7 = 28, the answer is 3.

What does 'bring down' mean in long division?

After subtracting, you bring down the next digit from the dividend to continue dividing. It's like moving the digit down to join your remainder.

How do I check if my long division answer is correct?

Multiply your answer by the divisor: $36 \times 7 = 252$ . If you get the original dividend back, your answer is correct!

What if I have a remainder at the end?

If there's a remainder and no more digits to bring down, your answer includes that remainder. For example, if you had remainder 3, you'd write 36 R3.

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