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Is sort of like multiples and dividing, when you divide a number by another which equals a whole number eg. divisable by 4- the last two digits can be divide by 4 eg. 3412

see 12 can 4 go into 12 yes so this means 3412 is divisable by 4

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Divisibility rules…

2: All even numbers are divisible by 2.

3: Sum up all the digits. If the result is divisible by 3 the so is the original number.

4: If the last 2 digits are divisible by 4 then the original number is.

5: If it ends in 5 or 0 it’s divisible by 5.

6: If it’s divisible by 2 and 3 then it’s divisible by 6.

7: If you double the last digit and subtract it from the rest of the number and the is 0 or divisible by 7.

8: Last 3 digits are divisible by 8

9: The sum of the digits is divisible by 3.
10: If it ends in 0 its divisible by 10.

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divisibility by 11. Subtract the last digit

from the remaining leading truncated number. If the result is divisible by 11, then so was the first number. Apply this rule over and over again as necessary.
Example: 19151--> 1915-1 =1914 -->191-4=187 -->18-7=11, so yes, 19151 is divisible by 11.

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Divisibility Rules

Divisible By:

If:

Examples:

2

The last digit is even [0,2,4,6]

128 is.

129 is NOT.

3

The sum of the digits is divisible by 3.

381 [3+8+1=12 and 12÷3=4] YES.

217 [2+1+7=10, and 10÷3 = 3 ⅓]  NO.

4

The last 2 digits are divisible by 4.

1312 is (12÷4=3)

7019 is not.

5

The last digit is 0 or 5.

175 is

809 is not

6

The number is divisible by both 2 and 3.

114 [It is even, and 1+1+4=6 and 6÷32]

Yes

308 [It is even, but 3+0+8=11 and 11÷3 = 3 ⅔]  No

7

If you double the last digit and subtract it from the rest of the number and the answer is:

0, or

divisible by 7

(Note: you can apply this rule to that answer again if you want)

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No

8

The last 3 digits are divisible by 8.

109816 (816÷8=102) Yes

216302 (302÷8=37 3/4) No

9

The sum of the digits is divisible by 9

(Note: you can apply this rule to that answer again if you want)

1629 (1+6+2+9=18, and again, 1+8=9) Yes

2013 (2+0+1+3=6) No

10

The number ends in 0

220 is

221 is not

11

If you sum every second digit and then subtract all other digits and the answer is:

0, or

divisible by 11

1364 ((3+4) - (1+6) = 0) Yes

3729 ((7+9) - (3+2) = 11) Yes

25176 ((5+7) - (2+1+6) = 3) No

12

The number is divisible by both 3 and 4

648 (By 3? 6+4+8=18 and 18÷3=6 Yes. By 4? 48÷4=12 Yes)  Yes 524  (By 3? 5+2+4=11, 11÷3= 3 2/3 No. Don't need to check by 4.) No

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Dividing by 2:
All all numbers ending in 0,2,4,6 or 8 (even numbers) are divisible by 2.

Dividing by 3 and 9:Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 3, so is the number.
3 example: 31212 (3+1+2+1+2=9) 9 is divisible by 3, so 12123 is too.
9 example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, so 43785 is too! Dividing by 4:

Are the last two digits in your number divisible by 4?
If so, the number is too.
For example: 45412 ends in 12 which is divisible by 4 which means 45412 can be too.

Dividing by 5:

Numbers ending in a 5 or a 0 are always divisible by 5.

Dividing by 6:

If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7:

Take the last digit in a number. Double and subtract the last digit in your number from the rest of the digits. Repeat the process for larger numbers. Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.
Dividing by 8

If the last 3 digits are divisible by 8, so is the entire number.
Example: 6008 - The last 3 digits are divisible by 8, so is 6008.

Dividing by 10
If the number ends in a 0 it is divisible by 10.

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If it is divisible by 2 then the last digit will

be even

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Any number that ends in 0, 2,4,6,8

is always divisible by 2

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Number 8: This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

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1. 2 =All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

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Numbers ending in 5 or 0 are always divisible

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if you

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Dividing by 2

You can divide all even numbers by 2. If it doesn’t end with 0,2,4,6 or 8, it isn’t divisible by 3.

Dividing by 3

Add up all the digits in the number.  E.g; 1263 (1+2+6+3=12) 12 ÷  3 = 4

If the answer is divisible by 3, so is the original number.

Dividing by 4

If the last two digits in your number are divisible, the whole number is.

Example: 358912 ends in 12 which is divisible by 4, so then, that makes 358912 divisible by 4.

Dividing by 5

Numbers ending in a 5 or a 0 can always be divided into 5.

Dividing by 6

If the number is divisible by 2 and 3, it’s divisible by 6 as well.

Dividing by 7

Take the very last number.

Double the last number, then subtract it from the rest.

Example: 357 (Double 7 is 14. 35 - 14 = 21. 21 is divisible by 7, so,  357 is divisible by 7.

Dividing by 8

If the last 3 digits are divisible by 8, so is the rest of the number.

Example: 6008 - The last 3 digits are divisible by 8, so, 6008 is too.

Dividing by 9

Add up all the digits in the number.

Find out what the answer is. If the answer is divisible by 9, so is the rest of the number.

Example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, so 43785 is too.

Dividing by 10
If the number ends in a 0, it is divisible by 10.

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Dividing by 2

1. All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Dividing by 3

1. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 3, so is the number

3. For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

Dividing by 4

1. Are the last two digits in your number divisible by 4?

2. If so, the number is too!

3. For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

Dividing by 5

1. Numbers ending in a 5 or a 0 are always divisible by 5.

Dividing by 6

1. If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7 (2 Tests)

Take the last digit in a number.

Double and subtract the last digit in your number from the rest of the digits.

Repeat the process for larger numbers.

Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

NEXT TEST

Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary

Add the products.

If the sum is divisible by 7 - so is your number.

Example: Is 2016 divisible by 7?

6(1) + 1(3) + 0(2) + 2(6) = 21

21 is divisible by 7 and we can now say that 2016 is also divisible by 7.

Dividing by 8

1. This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.

2. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

Dividing by 9

1. Almost the same rule and dividing by 3. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 9, so is the number.

3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

Dividing by 10

1. If the number ends in a 0, it is divisible by 10.

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All even numbers are divisible by 2 eg;

If they end in 2,4,6 or 8

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Dividing by 2

1. All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Dividing by 3

1. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 3, so is the number

3. For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

Dividing by 4

1. Are the last two digits in your number divisible by 4?

2. If so, the number is too!

3. For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

Dividing by 5

1. Numbers ending in a 5 or a 0 are always divisible by 5.

Dividing by 6

1. If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7

Take the last digit in a number.

Double and subtract the last digit in your number from the rest of the digits.

Repeat the process for larger numbers.

Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

NEXT

Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary

Add the products.

If the sum is divisible by 7 - so is your number.

Example: Is 2016 divisible by 7?

6(1) + 1(3) + 0(2) + 2(6) = 21

21 is divisible by 7 and we can now say that 2016 is also divisible by 7.

Dividing by 8

1. This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.

2. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

Dividing by 9

1. Almost the same rule and dividing by 3. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 9, so is the number.

3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

Dividing by 10

1. If the number ends in a 0, it is divisible by 10.

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Dividing by 7
Take the last digit in a number.
Double and subtract the last digit in your number from the rest of the digits.
Repeat the process for larger numbers.
Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

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2 can be divided if the last digit is even.

3 can be divided if the sum of the digits is able to be divided by 3

4 can be divided if the last two digits can be divided by four.

5 can be divided if the number ends in 5 or 0

6 can be divided if it can also be divided by both 2 and 3

7 can be divided if you double the last digit and subtract it from the rest of the number and the answer is either 0 or divisble by 7

8 can be divided if the last 3 digits are divisble by 8

9 can be divided if the sum of digits is divisible by 9

10 can be divided if the number ends in 0

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Dividing by 9

1. Almost the same rule and dividing by 3. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 9, so is the number.

3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

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The last digit is even

The last 3 digits are divisible by 8

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The rule for 2 :

Any whole number that ends in 0, 2, 4, 6, or 8

is divisible by 2.

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all even numbers can be divisible by 2

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2- The last digit is always even.

5- The last digit is always 0 or 5.

6- The number is both divisible by 2 and 3.

10- The number ends in 0.

12- The sum is both divisible by 3 and 4.

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Dividing by 3
Add up all the digits in the number.
Find out what the sum is. If the sum is divisible by 3, so is the number
For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

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Dividing by 2

1. All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Dividing by 3

1. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 3, so is the number

3. Dividing by 4

1. Are the last two digits in your number divisible by 4?

2. If so, the number is too!

3. For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

Dividing by 5

1. Numbers ending in a 5 or a 0 are always divisible by 5.

Dividing by 6

1. If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7 (2 Tests)

Take the last digit in a number.

Double and subtract the last digit in your number from the rest of the digits.

Repeat the process for larger numbers.

Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

Take the number and multiply each digit beginning on the right hand side (ones) by 1, 3, 2, 6, 4, 5. Repeat this sequence as necessary

Add the products.

If the sum is divisible by 7 - so is your number.

Example: Is 2016 divisible by 7?

6(1) + 1(3) + 0(2) + 2(6) = 21

21 is divisible by 7 and we can now say that 2016 is also divisible by 7.

Dividing by 8

1. This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number.

2. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

Dividing by 9

1. Almost the same rule and dividing by 3. Add up all the digits in the number.

2. Find out what the sum is. If the sum is divisible by 9, so is the number.

3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

Dividing by 10

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Divisible by

If:

2

If the last digit is even (0,2,4,6,8)eg.178

3

The sum of the digits is divisible by 3 e.6 243(2+4+3=9)

4

The last 2 digits are divisible by 4 e.g 516

5

The last digit is 0 or 5 e.g 4730

6

The number is divisible by both 2 and 3 e.g 312

7

If you double the last digit and subtract it from

the rest of the number and the answer is 0 or divisible by 7

e.g 672(double 2 is 4,67-4=63

8

The last 3 digits are divisible by 8

e.g 9816

9

The sum of all the digits is divisible by 9

e.g 207(2+7)

10

The number ends with a 0

8600

11

If you sum every second digit and then subtract all other digits

and the answer is 0 or divisible by 11 3729 (7+9)-(3+2)=11

12

The number is divisible by both 3 and 4

e.g 648

648 is divisible by 12 (6+4+8=18÷3=6)

(48÷4=12)

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The Divisibility rule for three

-If you add up all of the digits in that number and the answer is divisible by three then that means the number is too! e.g. 3451 3+4+5+1= 12 12 is divisible by zero!

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rule for 7. Duble the last number subtract from

the rest

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The Divisibility rules of 3.

Add the digits of the number you are dividing.

If it is a multiple of 3, then it is dividable by