Divisibility Rules

In this section, we learn about the divisibility rules for the numbers 2 through 12. When we say a number is "divisible by" another, this means there is no remainder involved in the division. The divisibility rules allow us to quickly determine if a given number is divisible by one of the numbers on the list: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. Having this tool, allows us to factor large numbers more efficiently.
Divisibility Rules 2 - 12:

• Divisibility by 2 - The number is even (ends with 0,2,4,6, or 8)
• Divisibility by 3 - Summing the digits of the number, produces a number that is divisible by 3
• Divisibility by 4 - Final two digits of the number, produces a number that is divisible by 4
• Divisibility by 5 - The number ends with a 0 or 5
• Divisibility by 6 - The number is divisible by both 2 and 3
• Divisibility by 7 - Remove 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 8 - Final three digits of the number, produces a number that is divisible by 8
• Divisibility by 9 - Summing the digits of the number, produces a number that is divisible by 9
• Divisibility by 10 - The number ends with a 0
• 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 - If the result is a 0 or a number that is divisible by 11, then the original number is divisible by 11
• Divisibility by 12 - The number is divisible by both 3 and 4