Practice Objectives

- Demonstrate the ability to determine if a number is divisible by 2 » 12

## Practice the Divisibility Rules for 2 » 12

Instructions:

Answer 7/10 questions correctly to pass.

Determine if the given number is divisible by .

Problem:

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Divisibility Rules 2 » 12:

- A number is divisible by 2 if the number is even
- The final digit of the number is a (0, 2, 4, 6, or 8)

- A number is divisible by 3 if the sum of the number's digits is divisible by 3
- A number is divisible by 4 if it is even and the final two digits of the number form a number that is divisible by 4
- A number is divisible by 5 if the final digit is a 0 or a 5
- A number is divisible by 6 if the number is divisible by both 2 and 3
- A number is divisible by 8 if it is even and the final three digits of the number form a number that is divisible by 8
- A number is divisible by 9 if the sum of the number's digits is divisible by 9
- A number is divisible by 10 if the final digit is a 0
- A number is divisible by 12 if the number is divisible by both 3 and 4

Divisibility by 7:

- We start by removing the final digit from the number, double the number and subtract it away from the shortened original number
- If the number formed is a 0 or a number that is divisible by 7, the original number is divisible by 7. We can repeat the process as needed

Divisibility by 11:

- Form the sum of the digits in the odd places and subtract away the sum of the digits in the even places
- The odd places refer to the 1st digit, 3rd digit, 5th digit, and so on
- The even places refer to the 2nd digit, 4th digit, 6th digit, and so on
- Note, we can count our digits starting from right to left or left to right. This can result in a sign difference, which is not important
- If the result is a 0 or a number that is divisible by 11, then the original number is divisible by 11

Step-by-Step:

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