Home > Pre-Algebra > Whole Numbers > Dividing Larger Whole Numbers

## Dividing Larger Whole Numbers

#### Introduction

If you have two large numbers to divide, you can use long division to do it without using a calculator. Once you know how to use long division, you will be able to do it for large numbers using exactly the same steps.

## Lesson

To do long division, you'll need to follow the same steps every time.

Let's take the sum 984 ÷ 6 = ?

To do this, we first write the sum like this:

6)$overline{984}$

We approach long division from the left (unlike most other processes in math, like addition, subtraction, and multiplication).

The first question we need to ask is how many times 6 goes into 9 (the first digit on the left). 6 goes into 9 once, so we can put a 1 above the 9 in the problem.

1 6)$overline{984}$

Then, because 1 x 6 is 6, we need to place that underneath the 9:

1 6)$overline{984}$  - 6

Now, we do 9 - 6 to find out what we have left. We also bring down the next digit to the right.

1 6)$overline{984}$  - 6     38

Now we work out how many times 6 goes into 38. Since 6 x 6 = 36, the answer is 6, with 2 remainder. We, therefore, follow the same process as before (put 6 above the line and write the result below, along with the next digit):

16 6)$overline{984}$  - 6     38   - 36         24

Finally, we are left with 24. We need to work out how many times 6 goes into 24. Since 6 x 4 = 24, the answer is 4, with no remainder. Therefore, we place the 4 on top of the sum, and we are done.

164 6)$overline{984}$  - 6     38   - 36         24

If we had a remainder from the final sum, we have two options. We can either keep it separate and write the answer as 'result and remainder' (for example 23 remainder 5).

Alternatively, we can add in a decimal point and 0 after the ones column, and keep going with the long division until we get to no remainder left. The only potential issue here is that we don't always know we will get rid of the remainder. If we have a recurring number, there is no situation where there is no remainder.

## Examples

$150 \div 25$
 25 1 5 0

 6 25 1 5 0

 6 25 1 5 0 - 1 5 0

 6 25 1 5 0 - 1 5 0 0