Shortcuts for Divisibility by 5, 6 , 8 and 9

Few shortcuts to help you work smartly and save time

Divisibility by 5:
How to check a number is divisible by 5?
It is very simple, check for units digit, if it is either 5 or 0, then clearly the number is divisible by 5.

Examples:
Is the number 13356890 divisible by 5?
Check the units digit in the given number
unit digit is 0, so 13356890 is divisible by 5.

Is the number 56722368553 divisible by 5?
The units digit is not 0 or 5, so the number 56722368553 is not divisible by 5.

Divisibility by 6:
How to check a number is divisible by 6?
It is very simple, check the number is divisible by 2 and 3, if it is divisible by both, then clearly the number is divisible by 6.

Examples:
Is the number 3246546 divisible by 6?
First check the number is divisible 2,
its unit digit is 6, which is divisible by 2.
Then check the number is divisible 3 also,
3 + 2 + 4 + 6 + 5 + 4 + 6 = 30
30 is divisible by 3, so the number is also divisible by 3
The number 3246546 is divisible both by 2 and 3, so it is divisible by 6.

Is the number 128956 divisible by 6?
Its unit digit is 6, which is divisible by 2.
Now check the number is divisible 3 also,
1 + 2 + 8 + 9 + 5 + 6 = 31
31 is not divisible by 3, so the number is not divisible by 3
The number 128956 is divisible only by 2 and not by 3, so it is not divisible by 6

Divisibility by 8:
How to check a number is divisible by 8?
It is very simple, check whether the last three digits of the number is divisible by 8, if it is, then the number is divisible by 8.

Examples:
Is the number 7377473496 divisible by 8?
Take the last three digits of the number.
Last three digit is 496, check whether it is divisible by 8.
496 is divisible by 8, So the number 7377473496 is divisible by 8.

Is the number 546632318 divisible by 8?
The last three digit is 318.
318 is not divisible by 8, so the number 546632318 is not divisible by 8.

Divisibility by 9:
How to check a number is divisible by 9?
It is very simple, first sum all the digits of the number, now check whether the result is divisible by 9. If the answer is divisible by 9, clearly the number will be divisible by 9. It is similar to divisibility of 3.

Examples:
Is the number 57225834 divisible by 9?
Now, sum the digits of the number,
5 + 7 + 2 + 2 + 5 + 8 + 3 + 4 = 36
36 is divisible by 9, so 57225834 is divisible by 9.

Is the number 3216763132 divisible by 3?
3 + 2 + 1 + 6 + 7 + 6 + 3 + 1 + 3 + 2 = 34
34 is not divisible by 9, so the number 3216763132 is not divisible by 9.

Source: http://www.helpwithassignment.com

Shortcuts for Divisibility by 2,3 and 4

Here are a set of time saving divisibility shortcuts that you can use:

Divisibility by 2:

How to check a number is divisible by 2?
It is very simple, first we should check the units digit of the number, whether it is divisible by 2. A number is divisible by 2, only when its unit digit contains 0, 2, 4, 6, 8.

Examples:
Is the number 6542646882 divisible by 2?
Now, check the units digit of the number, it is 2, so 6542646882 is divisible by 2.

Divisibility by 3:
How to check a number is divisible by 3?
It is very simple, first sum all the digits of the number, now check whether the result is divisible by 3. If the answer is divisible by 3, clearly the number will be divisible by 3.

Examples:
Is the number 6466545 divisible by 3?
Now, sum the digits of the number,
6 + 4 + 6 + 6 + 5 + 4 + 5 = 36
36 is divisible by 3, so 6466545 is divisible by 3.

Is the number 544733369 divisible by 3?
5 + 4 + 4 + 7 + 3 + 3 + 3 + 6 + 9 = 44
44 is not divisible by 3, so the number 544733369 is not divisible by 3.

Divisibility by 4:
How to check a number is divisible by 4?
It is very simple, first check the last two digits of the number is divisible by 4, then the number will be divisible by 4.

Examples:
Is the number 98731812 divisible by 4?
Take the last two digits in the given number,
Last two digit is 12, which is divisible by 4,
So 98731812 is divisible by 4.

Is the number 3426941365 divisible by 4?
The last two digit of the number is 65, which is not divisible by 4,
So the number 3426941365 is not divisible by 4.

Source: http://www.helpwithassignment.com

Multiplying by 25 and 125

To multiply by 25 you multiply by 100 (just add two 0’s to the end of the number) then divide by 4, since 100 = 25×4. Note: to divide by 4 your can just divide by 2 twice, since 2×2 = 4.

64×25 = 6400/4 = 3200/2 = 1600.

58×25 = 5800/4 = 2900/2 = 1450.

To multiply by 125, you multiply by 1000 then divide by 8 since 8×125 = 1000. Notice that 8 = 2×2x2. So, to divide by 1000 add three 0’s to the number and divide by 2 three times.

32×125 = 32000/8 = 16000/4 = 8000/2 = 4000.

48×125 = 48000/8 = 24000/4 = 12000/2 = 6000.

Source: http://www.helpwithassignment.com

The 11 Rule

To multiply any two digit number by 11:

For this example we will use 34.

· Separate the two digits in you mind (3__4).

· Notice the hole between them!

· Add the 6 and the 4 together (3+4=7)

· Put the resulting 7 in the hole 374. That's it! 11 x 34=374

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627

Source: http://www.helpwithassignment.com