Division by 4 and 8
In the last session on maths we introduced rules for dividing numbers by 3 and 9.
Here we continue to find rules for helping us with larger number and to see if they are divisible by 4 and 8.
We will start with 4 to introduce the idea of using multiples.
Don't worry if you don't know what that is at the moment you will soon get used to it.
Tests of divisibility
Or how can we tell if a number can be divided exactly by another
number?
What we are going to show you today are things you can and should use everyday to see if you can divide number by other numbers.
In fact these rules must be used regularly to be effective.
Before we discuss divisibility we need to look at multiples.
The following are multiples of 4:
| 4 | 8 | 12 | 16 | 20 | 24 |
Can you see the pattern?
Answer
Did you get it?
Any number that appears on the four times table (and beyond) is a multiple of 4. If four goes into a number exactly it is a multiple of four.
Divisibility by 4
Example:
How can we tell if a number can be divided exactly by 4?
Let's look at the table and see if just by looking at the numbers you can tell any are not divisible by
4:
| Number | Divisible by 4? | Reason |
| 386 | No | ? |
| 812 | Yes | |
| 7843 | No | odd |
| 9264 | Yes | |
| 3456784 | Yes | |
| 45372 | Yes | |
| 7832 | Yes | |
| 136 | Yes | |
| 715 | No | odd |
If the last digit is odd then it can't be divided by 4.
This does not help us with even numbers to see if they are divisible by four?
There is a quick and easy way!
Look at the table underneath showing the same numbers and see if the bold numbers show you anything?
| Number | Divisible by 4? | Reason |
| 386 | No | ? |
| 812 | Yes | |
| 7843 | No | odd |
| 9264 | Yes | |
| 3456784 | Yes | |
| 45372 | Yes | |
| 7832 | Yes | |
| 136 | Yes | |
| 715 | No | odd |
This is the key:
IF the last two digits of a number are a multiple of 4 then the number is divisible by 4
So look at the number: 456,756,432
Is this divisible by 4?
Look at the last two digits: 32. Is 32 a multiple of 4? YES.
This means that 456,756,432 is divisible by 4!
That was easy wasn't it?
Try these and see how quickly you can work out if these numbers are divisible by 4:
| Number | Divisible by 4? | How many 4s? |
| 488 | ||
| 714 | ||
| 326 | ||
| 1,896 | ||
| 78,664 | ||
| 45322 | ||
| 7852 | ||
| 134 | ||
| 868 |
| Number | Divisible by 4? | How many 4s? |
| 488 | Yes | 122 |
| 714 | No | |
| 326 | No | |
| 1,896 | Yes | 474 |
| 78,664 | Yes | 19666 |
| 45322 | No | |
| 7852 | Yes | 1963 |
| 134 | No | |
| 868 | Yes | 217 |
It is not hard to use this system for the next rule.
Dividing by 8
The rule for divisibility by 4 is, if the last two digits are a multiple of 4,
then the number is divisible by 4.
Divisibility by 8 is almost the same
IF the last three digits of a number are a multiple of 8 then the number is divisible by 8
Example:
Take the number 456,756,432
Is this divisible by 8?
Look at the last three digits: 432. Is 432 a multiple of 8? YES (54 X 8 )
This means that 456,756,432 is divisible by 8
Try these and see how quickly you can work out if these numbers are divisible by 8:
| Number | Divisible by 8? | How many 8s? |
| 488 | ||
| 714 | ||
| 326 | ||
| 1,896 | ||
| 78,664 | ||
| 45322 | ||
| 7852 | ||
| 134 | ||
| 868 |
| Number | Divisible by 8? | How many 8s? |
| 488 | Yes | 61 |
| 714 | no | |
| 326 | no | |
| 1,896 | Yes | 237 |
| 78,664 | Yes | 9833 |
| 45322 | no | |
| 7852 | no | |
| 134 | no | |
| 868 | no |
Those are our rules for quickly finding if a number is divisible by 4 or 8. You will see that it is harder for finding divisibility by 8 than 4.
Both these rules, if used regularly, will help you to be confident with numbers and enable you to see other interesting patterns.
Next time we will introduce rules to help you with both 7 and 11.
Good luck!