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Divisibility Rules

**Dividing by 2**

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

**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!

**Dividing by 4**

- Are the last two digits in your number divisible by 4?
- If so, the number is too!
- For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

**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 (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**

- 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.

**Dividing by 9**

- Almost the same rule and dividing by 3. Add up all the digits in the number.
- Find out what the sum is. If the sum is divisible by 9, so is the number.
- For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

**Dividing by 10**

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

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