Divisibility Rules 2 » 12 Practice

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: