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How to Do Long Division

Long division is super easy because you just do the same four steps over and over. Once you know how to do those basic steps once, repeating them is super easy. 

On this page, I'll explain each of the four steps and work through a visualized example.

You'll need to be familiar with these vocabulary words:

Dividend: The number that is being divided. The dividend tells you the number of things in your original group. 

Divisor: The number that the dividend is being divided by. The divisor tells you how many smaller groups the things in your original group are going to be equally divided among. 

Quotient: The "answer". The quotient tells you how many things are in each of the smaller groups after you finish dividing the things equally. 

If you need more information about how to write remainders or if you want to see how to do long division with decimals or polynomials, check out these other pages:

How to Write Remainders

(Click Here)

Long Division with Decimals

(Click Here)

Long Division with Polynomials

(Click Here)

Long Division Steps

  1. Place Value - Identify the largest place value in the dividend. This is the place value you'll work on for the first round of long division. It will also determine how many rounds of long division you need to do. 
  2. Divide - Divide the dividend (only the place value you're working on) by the divisor. It's OK if it doesn't divide evenly. In the corresponding place value of the quotient, write the number of times the divisor goes into the dividend.  
  3. Multiply - Multiply the divisor by the quotient number you found in Step 2.
  4. Subtract - Subtract the result of Step 3 from the dividend. If there are any left-overs for the place value you're working on, you'll convert them over to the next place value in the next step. 
  5. Next Place Value - Move on to the next largest place value. Convert any left-overs from the last place value into the new place value and repeat all of the steps above.

The number of times that you'll repeat these steps depends on how many place values your dividend has.

If your largest place value is the hundreds place, you'll do three rounds of long division. If your largest place value is the ten thousands place, you'll do five rounds of long division. 

Long Division Example:
\(415\div3\)

In this example, 415 is the dividend and 3 is the divisor. To find the quotient, we need to divide 415 equally into 3 groups. 

There are three place values (hundreds, tens, and ones) in the divisor so we will work through the long division process three times.

At the end of each round of long division, I'll give you a picture to help you visualize what we accomplished during that round. 

To start off, let's look at the visualization for the original problem. 

415 can be visualized as 4 hundred blocks, 1 ten block, and 5 one blocks. All of these blocks are currently in a "to be divided" pile.

As we work through the long division process, we will divide these blocks equally into 3 groups, starting with the hundreds. 

Hundreds Place Value

STEP 1:

Place Value

The largest place value in this problem is the 4 in the hundreds place value.

STEP 2:

Divide

How many times does 3 go into 4? 1 time.

So, we can put 1 hundred in each of the three groups and write a 1 in the hundreds place of our quotient.

STEP 3:

Multiply

1 hundred times 3 is 300

This means that we will take a total of 3 hundreds out of the "to be divided" pile when we put 1 hundred in each of the three groups. 

STEP 4:

Subtract

415 minus 300 is 115

This means that we have 1 hundred, 1 ten, and 5 ones left in our "to be divided" pile after we take out the 3 hundreds.

The left-over hundred will be converted into tens during the next round of long division. 

After we finish the long division process for the hundreds place value, we have 1 hundred in each of our three groups and 115 in our "to be divided" pile.

Next, we will do the long division process for the tens place value.

Tens Place Value

STEP 1:

Place Value

The next largest place value in this problem is the 1 in the tens place.

When we convert the left-over 1 hundred from the last round into 10 tens, we have a total of 11 tens.

STEP 2:

Divide

How many times does 3 go into 113 times.

So, we can put 3 tens in each of the three groups and write a 3 in the tens place of our quotient.

STEP 3:

Multiply

3 tens times 3 is 90

This means that we'll take a total of 9 tens out of the "to be divided" pile when we put 3 tens in each of the three groups. 

STEP 4:

Subtract

115 minus 90 is 25

This means that we have 2 tens, and 5 ones left in our "to be divided" pile after we take out the 9 tens.

After we finish the long division process for the tens place value, we have 1 hundred and 3 tens in each of our three groups and 25 in our "to be divided" pile.

Now we'll do the long division process for the ones place value. It's the last round of long division for this problem...yay!

Ones Place Value

STEP 1:

Place Value

The next largest place value in this problem is the 5 in the ones place value.

When we convert the left-over 2 tens into 20 ones, we have a total of 25 ones.

STEP 2:

Divide

How many times does 3 go into 258 times.

So, we can put 8 ones in each of the three groups and write an 8 in the ones place of our quotient.

STEP 3:

Multiply

8 ones times 3 is 24

This means that we'll take a total of 24 ones out of the "to be divided" pile when we put 8 ones in each of the three groups. 

STEP 4:

Subtract

25 minus 24 is 1

This means that we have 1 one left in our "to be divided" pile. This is our remainder because we do not have any more place values to divide by.

So, that means that when we divide 415 into 3 groups, we end up with 138 in each group and a remainder of 1. Ta da!

Question

Answer

What is a remainder? 

Click here to learn about all the different ways you can write remainders.

Resources

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