Sometimes, when we divide numbers, we find that they don’t split evenly into whole numbers. Take 13 ÷ 2, for example—2 goes into 13 exactly 6 times, but there’s something left over: a remainder.
Figuring out the remainder for two-digit numbers is simple because we can use multiplication facts, but what about when we divide a three-digit number by a one-digit number, like 238 ÷ 3?
Let’s take a closer look.
This simple guide is for anyone looking to learn and master long division with remainders, from elementary schoolers who need a little extra help in their class to test-takers and anyone looking to brush up on their skills.
Read on to find clear definitions, easy-to-follow steps, helpful examples, and practice problems to test your skills.
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Long division is a method we use to break the division of large numbers into smaller, more manageable parts.
To see how long division with remainders works, let’s remember what its components are.
Let’s take an example: 238 ÷ 3. When we divide, we get 79 R1—where:
238 is the dividend (the number being divided)
3 is the divisor (the number we are dividing by)
79 is the quotient (the answer)
1 is the remainder (what’s left over)
What we can notice here is that, unlike a calculator that often gives us a decimal answer, long division keeps the remainder separate, showing exactly what is left over after division.
And the long division process?
Long division is usually centered around four key operations:
Divide: Starting from the left, find how many whole times the divisor fits into the first digit (or group of digits) of the dividend.
Multiply: Multiply the quotient digit by the divisor and write the product below the digit (or group of digits) used for division.
Subtract: Subtract to find what’s left over.
Bring Down: Bring down the next digit of the dividend and repeat the steps until all digits have been used. If there’s anything left over, that’s the remainder.
If you need a refresher on any of the steps, check out our step-by-step guide to long division for a detailed walkthrough.
At Mathnasium, we love to teach and learn new concepts through examples, walking through the steps together.
Let’s see how long division with remainders works with this example:
We’ll divide 916 by 5.
Before we begin with the operations, let’s make sure we place 916 (the dividend) inside the division symbol and 5 (the divisor) outside, on the left, like so:
Now, let’s see the steps.
Step 1: Divide
Find the number of whole 5s that are inside of 9.
Since 5 × 1 = 5 and 5 × 2 = 10, we can conclude that 5 fits into 9 once.
Write 1 above 9 in 916 and continue the division process.
Step 2: Multiply & Subtract
Find the product of 5 and 1.
5 × 1 = 5
Write the result (5) below 9 and subtract it from 9.
9 — 5 = 4
Write the result below.
Step 3: Bring Down
Bring down the 1, creating a new number with what was left over from the previous step.
Step 4: Divide Again
Find the number of whole 5s that are inside of 41.
Since 5 × 8 = 40, we know that 5 fits into 41 eight times.
Write 8 in the quotient above 1 in 916.
Step 5: Multiply & Subtract Again
Find the product of 5 and 8.
5 × 8 = 40
Write 40 below 41, then subtract it from 41.
41 — 40 = 1
Write the result (1) below.
Step 6: Bring Down Again
Bring down 6, making a new number with what was left over from the previous step.
Step 7: Divide Again
Find the number of whole 5s that are inside of 16.
Since 5 × 3 = 15, we know that 5 fits into 16 three times.
Write 3 in the quotient, right above 6 in 916.
Step 8: Multiply & Subtract Again
Find the product of 5 and 3.
5 × 3 = 15
Write the result (15) below 16, then subtract it from 16.
16 — 15 = 1
Write the result (1) below.
Since there are no more digits to bring down, we have a remainder of 1.
We can write the final answer as:
916 ÷ 5 = 183 R1
And that’s how we perform long division with remainders.
Long division with remainders can look a little different depending on the numbers involved.
To make sure you’re ready for any situation, we’ll walk through a few different scenarios and show you how to solve them
Now, let’s go through another long division example. This time, we’ll deal with a case where the divisor is larger than the first digit of the dividend.
We’ll divide 762 ÷ 9
Before we go into the long division process, let’s place 762 (dividend) inside the division symbol and 9 (divisor) outside:
Step 1: Divide
Check how many whole 9s fit into 7. Since 9 can’t fit into 7, we move to the next digit in the dividend. Now, find how many whole 9s fit into 76.
Since 9 × 8 = 72, we know that 9 fits into 76 eight times.
Write 8 above 6 in 762.
Step 2: Multiply & Subtract
Find the product of 9 and 8.
9 × 8 = 72
Write the result (72) below 76, then subtract it from 76.
76 — 72 = 4
Write the result (4) below.
Step 3: Bring down
Bring down the 2, creating a new number with what was left over from the previous step.
Step 4: Divide Again
Find the number of whole 9s that are inside of 42.
Since 9 × 4 = 36, we know that 9 fits into 42 four times.
Write 4 in the quotient above 2 in 762.
Step 5: Multiply & Subtract
Find the product of 9 and 4.
9 × 4 = 36
Write the result (36) below 42, then subtract it from 42.
42 — 36 = 6
Write the result (6) below.
Since there are no more digits to bring down, we have a remainder of 6.
We can write the final result as:
762 ÷ 9 = 84 R6
Now, let’s go through a long division example where a zero appears in the quotient.
We'll solve 2146 ÷ 7.
Before we perform long division, we place 2146 (dividend) inside the division symbol and 7 (divisor) outside, on the left:
Step 1: Divide
Check how many whole 7s fit into 2. None. Move to the next digit in the dividend and find how many whole 7s fit into 21.
Since 7 × 3 = 21, we know that 7 fits into 21 three times.
Write 3 in the quotient above 1 in 2,146.
Step 2: Multiply & Subtract
Find the product of 7 and 3.
7 × 3 = 21
Write the result (21) below 21 and subtract it from 21.
Step 3: Bring down
Bring down the 4.
Step 4: Divide & Bring Down
Find the number of whole 7s that are inside of 4.
Since there are no 7s inside of 4, write a 0 in the quotient and bring down the 6.
Step 5: Divide Again
Find the number of whole 7s inside of 46.
Since 7 × 6 = 42, we know that 7 fits into 46 six times.
Write 6 in the quotient, right above 6 in 2,146.
Step 6: Multiply & Subtract
Find the product of 7 and 6.
7 × 6 = 42
Write the result (42) below 46 and subtract it from 46.
46 — 42 = 4
Write the result (4) below.
Since there are no more digits to bring down, we have a remainder of 4.
We can write the final answer as:
2146 ÷ 7 = 306 R4
Now, let’s see how to handle long division with a two-digit divisor. We’ll go through the steps for 201 ÷ 33.
When numbers get large, it can be helpful to round both the divisor and the dividend to help estimate the digits in the quotient.
33 rounds to 30
201 rounds to 200
Now, find how many whole 30s fit into 200.
30 goes into 200 about 6 times. Let’s check: 30 × 6 = 180.
This gives us a helpful estimate and a good place to start.
Sometimes, you may need one less or one more than your estimate, so we’ll adjust if necessary.
Now, we place 201 (dividend) inside the division symbol and 33 (divisor) outside, on the left:
We’re ready to perform long division.
Step 1: Divide
Using our estimate from earlier, we think that 33 goes into 201 a total of 6 times.
We write 6 as the last digit of our quotient.
Step 2: Multiply & Subtract
Find the product of 33 and 6.
33 × 6 = 198
Write the result (198) below 201 and subtract it from 201.
201 — 198 = 3
Write the result (3) below.
Since there are no digits to bring down, our remainder is 3.
We write the result as:
201 ÷ 33 = 6 R3
Work through these exercises to challenge your skills!
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