What do I do if the divisor doesn't fit into the first digit of the dividend?

Look at the first two digits instead. If the divisor still doesn't fit, look at the first three digits. Keep combining digits from the left until you have a number that the divisor can go into at least once. Make sure to write the first digit of your quotient above the correct place—above the last digit of the group you just divided.

How do I know when to write a zero in the quotient?

Write a zero in the quotient when the divisor doesn't fit into the number you brought down. For example, if you bring down a digit and now have 15, but your divisor is 23, you can't divide. Write a 0 in the quotient (in the correct position) and bring down the next digit. This keeps your quotient aligned correctly.

My remainder is bigger than the divisor. What did I do wrong?

You didn't divide enough times. If your remainder is larger than the divisor, that means the divisor fits into it at least once more. Go back and increase your quotient digit, then redo the multiplication and subtraction. Keep dividing until the remainder is smaller than the divisor.

Why do I need to check my division by multiplying?

Multiplication is the inverse (opposite) of division. When you multiply the quotient by the divisor and add the remainder, you should get back the original dividend. If you don't, you made a mistake somewhere in the long division. Checking catches errors early so you can fix them before moving on.

M6MATH-4.1

Dividing Multi-Digit Whole Numbers

Learn how to divide multi-digit whole numbers using long division, and verify answers by multiplying back with the divisor—an essential skill for working with larger numbers.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on Dividing Multi-Digit Whole Numbers, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start Dividing Multi-Digit Whole Numbers free

What this lesson covers

Division becomes much more powerful when you can tackle numbers that don't divide evenly in your head. In Grade 5, you probably divided smaller numbers or used division facts. Now you'll learn the standard long-division algorithm that works for any multi-digit whole number, and you'll discover how to check your work using multiplication. This skill is the foundation for dividing decimals later on, and it builds your confidence with all kinds of real-world problems—from sharing amounts fairly to measuring how many times one quantity fits into another.

Understanding Division with Remainders

When you divide one whole number by another, you may not get a whole number answer. Instead, you get a quotient (the main answer) and sometimes a remainder (what's left over). For example,

27 \div 5 = 5

remainder

2

, because

5 \times 5 = 25

, and

27 - 25 = 2

is what's left. You can write this as

27 \div 5 = 5\text{ R}2

or as

5\frac{2}{5}

(five and two-fifths). The remainder is always smaller than the divisor—if your remainder is bigger, you didn't divide enough times.

With multi-digit numbers, remainders work the same way. If you divide

348

6

, you're asking: how many groups of

6

fit into

348

? The answer is

58

groups with a remainder of

0

(since

6 \times 58 = 348

). The key insight is that the process stays the same whether you're dividing small or large numbers—you just repeat the steps more times.

The Long-Division Algorithm

Long division breaks the problem into smaller, manageable steps. You divide one digit (or group of digits) at a time, starting from the left.

Here's the repeating pattern: divide, multiply, subtract, bring down.

Start by looking at just the leftmost digits of the dividend until you have a number that the divisor goes into at least once. Divide that group by the divisor and write the quotient digit above. Multiply the quotient digit by the divisor and write the result below the digits you were dividing. Subtract to find what's left. Bring down the next digit and repeat.

For example, to divide

456 \div 12

:

The divisor

12

doesn't fit into

4

, so look at

45

. Twelve goes into

45

three times (

12 \times 3 = 36

). Write

3

above the

5

. Subtract:

45 - 36 = 9

. Bring down the

6

to make

96

. Twelve goes into

96

eight times (

12 \times 8 = 96

). Write

8

above the

6

. Subtract:

96 - 96 = 0

. Your quotient is

38

with no remainder.

When you reach the last digit and have a number smaller than the divisor, that becomes your remainder.

Checking Your Answer with Multiplication

The best way to verify division is to reverse it: multiply the quotient by the divisor and add the remainder. If this equals the original dividend, you're correct.

The relationship is:

\text{(Quotient} \times \text{Divisor)} + \text{Remainder} = \text{Dividend}

For the example above,

456 \div 12 = 38

with remainder

0

. Check:

(38 \times 12) + 0 = 456 + 0 = 456

. ✓

If you had divided incorrectly and gotten quotient

37

, your check would show:

(37 \times 12) + \text{R} = 444 + \text{R} = 456

, so

\text{R} = 12

. But a remainder can never be as large as the divisor, so you'd know something went wrong and could find the error.

This check is your safety net. Always multiply back; it takes just a few seconds and catches mistakes immediately.

Common Mistakes and How to Avoid Them

One frequent error is forgetting to bring down the next digit. After you subtract, you must bring down the very next digit from the dividend before dividing again. If you skip this step, your quotient will be way too small.

Another common mistake is writing the quotient digit in the wrong place. The quotient digit you write goes directly above the last digit of the group you just divided. If you move one place left or right, your final answer shifts by a power of ten.

Students also sometimes give a remainder that's larger than or equal to the divisor. Remember: if your remainder is

12

and your divisor is

12

, you can divide one more time. Keep dividing until the remaining number is smaller than the divisor.

Finally, be careful with zeros in the quotient. If the divisor doesn't fit into the next group of digits, you must write a

0

in the quotient (in the correct place) and bring down another digit. Skipping the zero will misalign everything that comes after.

Why This Matters Beyond Division

The long-division algorithm is not just about dividing whole numbers. It's the foundation for dividing decimals, which you'll learn soon. When you divide decimals, the process is identical—you just have to place the decimal point correctly in your answer. Understanding how and why long division works now means you won't struggle with decimals later.

Division also connects directly to fractions and ratios. When you divide to get a remainder and convert it into a fraction, you're building fraction sense. And in real situations—figuring out how many buses you need to transport students, calculating unit prices, or sharing amounts fairly—division with remainders is exactly what you need.

Key terms

Dividend.: The number being divided. In $456 \div 12$ , the dividend is $456$ .
Divisor.: The number you are dividing by. In $456 \div 12$ , the divisor is $12$ .
Quotient.: The result of division (the answer before the remainder). In $456 \div 12 = 38$ , the quotient is $38$ .
Remainder.: The amount left over after division when it doesn't divide evenly. In $27 \div 5 = 5\text{ R}2$ , the remainder is $2$ .
Long division.: A step-by-step algorithm for dividing multi-digit numbers: divide, multiply, subtract, and bring down.
Verify or check.: To confirm an answer is correct, usually by performing the inverse operation (multiplication, in the case of division).

Worked example

Divide

738 \div 15

and check your answer.

Step 1: Set up long division. Write

738

inside the division bracket and

15

outside to the left.

Step 2: Find where to start. Does

15

go into

7

? No. Does

15

go into

73

? Yes. Fifteen goes into

73

four times, because

15 \times 4 = 60

. Write

4

above the

3

in the quotient line.

Step 3: Multiply and subtract. Multiply:

15 \times 4 = 60

. Subtract:

73 - 60 = 13

. Write

13

below.

Step 4: Bring down the next digit. Bring down the

8

to make

138

.

Step 5: Divide again. How many times does

15

go into

138

? Try

9

15 \times 9 = 135

. Yes, that works. Write

9

above the

8

in the quotient line.

Step 6: Multiply and subtract. Multiply:

15 \times 9 = 135

. Subtract:

138 - 135 = 3

. Write

3

below.

Step 7: Check the remainder. Is

3

smaller than

15

(the divisor)? Yes. So you're done. The quotient is

49

with remainder

3

, written as

49\text{ R}3

.

Step 8: Verify. Use the check formula:

(\text{Quotient} \times \text{Divisor}) + \text{Remainder} = \text{Dividend}

(49 \times 15) + 3 = 735 + 3 = 738

. ✓ Correct!

Practice questions

Divide

624 \div 16

using long division and verify your answer.

Answer: The quotient is $39$ with remainder $0$ . Check: $(39 \times 16) + 0 = 624$ . ✓

Start by asking: does

16

go into

6

? No. Does

16

go into

62

? Yes,

3

times (

16 \times 3 = 48

). Subtract:

62 - 48 = 14

. Bring down the

4

to make

144

. Does

16

go into

144

? Yes,

9

times (

16 \times 9 = 144

). Subtract:

144 - 144 = 0

. Since the remainder is

0

, we write

39

with no remainder. To check, multiply

39 \times 16 = 624

, which matches the dividend.

A teacher has

856

pencils to share equally among

12

students. How many pencils does each student get, and how many are left over?

Answer: Each student gets $71$ pencils, and $4$ pencils are left over.

This is a division problem:

856 \div 12

. Using long division:

12

goes into

85

seven times (

12 \times 7 = 84

). Subtract to get

1

. Bring down the

6

to make

16

. Twelve goes into

16

once (

12 \times 1 = 12

). Subtract:

16 - 12 = 4

. The quotient is

71

with remainder

4

, which means each of the

12

students receives

71

pencils and

4

are left over. You can verify:

(71 \times 12) + 4 = 852 + 4 = 856

. ✓

Divide

2045 \div 23

. What is the quotient?

$87\text{ R}24$
$89$
$89\text{ R}8$
$88\text{ R}21$

Answer: $89$

Using long division:

23

doesn't go into

20

, so look at

204

. Twenty-three goes into

204

eight times (

23 \times 8 = 184

). Subtract:

204 - 184 = 20

. Bring down the

5

to make

205

. Twenty-three goes into

205

eight times... wait, let me recalculate.

23 \times 9 = 207

, which is too large.

23 \times 8 = 184

. Actually,

23 \times 9 = 207

, which exceeds

205

. Let me redo:

204

divided by

23

: try

8

23 \times 8 = 184

. Subtract:

204 - 184 = 20

. Bring down the

5

to make

205

. Now,

23 \times 8 = 184

(too small) and

23 \times 9 = 207

(too large for

205

). Actually

23 \times 9 = 207 > 205

, so use

8

. Wait:

23 \times 9 = 207

, and

205 < 207

, so we use

8

205 - 184 = 21

... Let me recalculate fully.

2045 \div 23

: Try

89

. Check:

89 \times 23 = (90 - 1) \times 23 = 2070 - 23 = 2047

. That's too large. Try

88

88 \times 23 = (90 - 2) \times 23 = 2070 - 46 = 2024

. Subtract:

2045 - 2024 = 21

. So the answer is

88\text{ R}21

. But that's option D. Let me recheck the problem... Actually,

89 \times 23

89 \times 20 = 1780

89 \times 3 = 267

. Total:

1780 + 267 = 2047

. That exceeds

2045

. Using

88

88 \times 23 = 2024

. Remainder:

2045 - 2024 = 21

. The correct answer is

88\text{ R}21

, which is choice D. However, the question states the answer should be

89

, which doesn't match. Let me verify once more: if the answer really is

89

, then

89 \times 23

should be close to

2045

. It equals

2047

, which is

2

more than

2045

. So

89

is too large. The correct answer should be option D:

88\text{ R}21

. There appears to be an error in the question as stated. For the purposes of this guide, the correct quotient is

88\text{ R}21

FAQ

What do I do if the divisor doesn't fit into the first digit of the dividend?: Look at the first two digits instead. If the divisor still doesn't fit, look at the first three digits. Keep combining digits from the left until you have a number that the divisor can go into at least once. Make sure to write the first digit of your quotient above the correct place—above the last digit of the group you just divided.
How do I know when to write a zero in the quotient?: Write a zero in the quotient when the divisor doesn't fit into the number you brought down. For example, if you bring down a digit and now have $15$ , but your divisor is $23$ , you can't divide. Write a $0$ in the quotient (in the correct position) and bring down the next digit. This keeps your quotient aligned correctly.
My remainder is bigger than the divisor. What did I do wrong?: You didn't divide enough times. If your remainder is larger than the divisor, that means the divisor fits into it at least once more. Go back and increase your quotient digit, then redo the multiplication and subtraction. Keep dividing until the remainder is smaller than the divisor.
Why do I need to check my division by multiplying?: Multiplication is the inverse (opposite) of division. When you multiply the quotient by the divisor and add the remainder, you should get back the original dividend. If you don't, you made a mistake somewhere in the long division. Checking catches errors early so you can fix them before moving on.

Learn this with a teacher, not a page

The Crimsora tutor teaches Dividing Multi-Digit Whole Numbers live — explaining on a whiteboard, asking you questions, and adapting to where you get stuck.

Try a live session free